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Volumn 79, Issue , 2010, Pages 1-288

Nonlinear partial differential equations: Asymptotic behavior of solutions and self-similar solutions

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EID: 84994139726     PISSN: 14211750     EISSN: 23740280     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (70)

References (270)
  • 1
  • 4
    • 0000147123 scopus 로고
    • Mean curvature flow through singularities for surfaces of rotation
    • [Altschuler Angenent Giga 1995] S. Altschuler, S. B. Angenent, and Y. Giga, Mean curvature flow through singularities for surfaces of rotation, J. Geom. Anal., 5 (1995), 293–358.
    • (1995) J. Geom. Anal. , vol.5 , pp. 293-358
    • Altschuler, S.1    Angenent, S.B.2    Giga, Y.3
  • 5
    • 84942222028 scopus 로고
    • The zero set of a solution of a parabolic equation
    • [Angenent 1988] S. B. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math., 390 (1988), 79–96.
    • (1988) J. Reine Angew. Math. , vol.390 , pp. 79-96
    • Angenent, S.B.1
  • 7
    • 21444444162 scopus 로고    scopus 로고
    • Degenerate neckpinches in mean curvature flow
    • [Angenent and Velázquez 1997] S. B. Angenent and J. J. L. Velázquez, Degenerate neckpinches in mean curvature flow, J. Reine Angew. Math., 482(1997), 15–66.
    • (1997) J. Reine Angew. Math. , vol.482 , pp. 15-66
    • Angenent, S.B.1    Velázquez, J.J.L.2
  • 8
    • 85045469618 scopus 로고    scopus 로고
    • The development of real analysis and its influence on analysis
    • (in Japanese)
    • [Arai 1998] H. Arai, The development of real analysis and its influence on analysis, Sûgaku, 50 (1998), 29–55 (in Japanese).
    • (1998) Sûgaku , vol.50 , pp. 29-55
    • Arai, H.1
  • 9
    • 84968488966 scopus 로고
    • Bounds for fundamental solutions of a parabolic equation
    • [Aronson 1968] D. G. Aronson, Bounds for fundamental solutions of a parabolic equation, Bull. Amer. Math. Soc., 73 (1968), 890–896.
    • (1968) Bull. Amer. Math. Soc. , vol.73 , pp. 890-896
    • Aronson, D.G.1
  • 13
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • [Beale Kato Majda 1984] J. T. Beale, T. Kato, and A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys., 94 (1984), 61–66.
    • (1984) Comm. Math. Phys. , vol.94 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 14
    • 0003329717 scopus 로고
    • Mathematical problems from combustion theory
    • Springer, New York
    • [Bebernes Eberly 1989] J. Bebernes and D. Eberly, Mathematical problems from combustion theory, Appl. Math. Sci., 83 Springer, New York (1989).
    • (1989) Appl. Math. Sci. , vol.83
    • Bebernes, J.1    Eberly, D.2
  • 15
    • 4644221655 scopus 로고    scopus 로고
    • Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations
    • [Benachour Karch Laurencot 2004] S. Benachour, G. Karch, and P. Laurencot, Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations, J. Math. Pures Appl., 83 (2004), 1275–1308.
    • (2004) J. Math. Pures Appl. , vol.83 , pp. 1275-1308
    • Benachour, S.1    Karch, G.2    Laurencot, P.3
  • 16
    • 21844500356 scopus 로고
    • Global solutions of two-dimensional Navier-Stokes and Euler equations
    • [Ben-Artzi 1994] M. Ben-Artzi, Global solutions of two-dimensional Navier-Stokes and Euler equations, Arch. Rational Mech. Anal., 128 (1994), 329–358.
    • (1994) Arch. Rational Mech. Anal. , vol.128 , pp. 329-358
    • Ben-Artzi, M.1
  • 18
    • 85045451316 scopus 로고    scopus 로고
    • Stability and dynamics of self-similarity in evolution equations
    • [Bernoff Witelski 2009] A. Bernoff and T. P. Witelski, Stability and dynamics of self-similarity in evolution equations, J. Eng. Math., on line (2009).
    • (2009) J. Eng. Math.
    • Bernoff, A.1    Witelski, T.P.2
  • 19
    • 22844457221 scopus 로고    scopus 로고
    • Similarity solutions of the generalized Korteweg-de Vries equations
    • [Bona Weissler 1999] J. L. Bona and F. B. Weissler, Similarity solutions of the generalized Korteweg-de Vries equations, Proc. Cambridge Publ. Soc., 127 (1999), 323–335.
    • (1999) Proc. Cambridge Publ. Soc. , vol.127 , pp. 323-335
    • Bona, J.L.1    Weissler, F.B.2
  • 20
    • 49149142420 scopus 로고    scopus 로고
    • Nonlinear Schrödinger evolution equations, Nonlinear Anal
    • [Brezis Gallouet 1980] H. Brezis and T. Gallouet, Nonlinear Schrödinger evolution equations, Nonlinear Anal. T.M.A., 4 (1980) 677–681.
    • T.M.A. , vol.4 , Issue.1980 , pp. 677-681
    • Brezis, H.1    Gallouet, T.2
  • 21
    • 0000628903 scopus 로고
    • A note on limiting cases of Sobolev embeddings and convolution inequalities
    • [Brezis Wainger 1980] H. Brezis and S. Wainger, A note on limiting cases of Sobolev embeddings and convolution inequalities, Comm. Partial Differential Equations, 5 (1980), 773–789.
    • (1980) Comm. Partial Differential Equations , vol.5 , pp. 773-789
    • Brezis, H.1    Wainger, S.2
  • 22
    • 0000877190 scopus 로고
    • Universality in blow-up for nonlinear heat equations
    • [Bricmont Kupiainen 1994] J. Bricmont and A. Kupiainen, Universality in blow-up for nonlinear heat equations, Nonlinearity, 7 (1994), 539–575.
    • (1994) Nonlinearity , vol.7 , pp. 539-575
    • Bricmont, J.1    Kupiainen, A.2
  • 23
    • 0013158824 scopus 로고
    • The existence of bounded solutions of a semilinear elliptic equation
    • [Budd Qi 1989] C. J. Budd and Y.-W. Qi, The existence of bounded solutions of a semilinear elliptic equation, J. Differential Equations, 82 (1989), 207–218.
    • (1989) J. Differential Equations , vol.82 , pp. 207-218
    • Budd, C.J.1    Qi, Y.-W.2
  • 25
    • 0000927436 scopus 로고
    • First order interpolation inequalities with weights
    • [Caffarelli Kohn Nirenberg 1984] L. Caffarelli, R. Kohn, and L. Nirenberg, First order interpolation inequalities with weights, Compositio Mathematica, 53 (1984), 259–275.
    • (1984) Compositio Mathematica , vol.53 , pp. 259-275
    • Caffarelli, L.1    Kohn, R.2    Nirenberg, L.3
  • 26
    • 34250593672 scopus 로고
    • On the existence of certain singular integrals
    • [Calderon Zygmund 1952] A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math., 88 (1952), 85–139.
    • (1952) Acta Math. , vol.88 , pp. 85-139
    • Calderon, A.P.1    Zygmund, A.2
  • 28
    • 0031322648 scopus 로고    scopus 로고
    • A generalization of a theorem by Kato on Navier-Stokes equations
    • [Cannone 1997] M. Cannone, A generalization of a theorem by Kato on Navier-Stokes equations, Rev. Mat. Iberoamericana, 13 (3) (1997) 515–541.
    • (1997) Rev. Mat. Iberoamericana , vol.13 , Issue.3 , pp. 515-541
    • Cannone, M.1
  • 29
    • 67649574180 scopus 로고    scopus 로고
    • Harmonic analysis tools for solving the incompressible Navier-Stokes equations
    • S.J. Friedlander and D. SerreChapter 3, Elsevier B.V
    • [Cannone 2004] M. Cannone, Harmonic analysis tools for solving the incompressible Navier-Stokes equations, Handbook of Mathematical Fluid Dynamics, Vol. III (edited by S.J. Friedlander and D. Serre), Chapter 3, Elsevier B.V. (2004), 161–244.
    • (2004) Handbook of Mathematical Fluid Dynamics , vol.3 , pp. 161-244
    • Cannone, M.1
  • 30
    • 62549111607 scopus 로고
    • Exposé n. VIII, Seminaire X-EDP, Ecole Polytechnique
    • 3, Exposé n. VIII, Seminaire X-EDP, Ecole Polytechnique (1994).
    • (1994) 3
    • Cannone, M.1    Meyer, Y.2    Planchon, F.3
  • 34
    • 84963043487 scopus 로고
    • Sharp constant in Nash’s inequality
    • [Carlen Loss 1993] E. A. Carlen and M. Loss, Sharp constant in Nash’s inequality, Internat. Math. Res. Notices, 7 (1993), 213–215.
    • (1993) Internat. Math. Res. Notices , vol.7 , pp. 213-215
    • Carlen, E.A.1    Loss, M.2
  • 35
    • 84974004482 scopus 로고    scopus 로고
    • Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation
    • [Carlen Loss 1996] E. A. Carlen and M. Loss, Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation, Duke Math. J., 81 (1996), 135–157.
    • (1996) Duke Math. J. , vol.81 , pp. 135-157
    • Carlen, E.A.1    Loss, M.2
  • 36
    • 0000163841 scopus 로고
    • Asymptotic behavior for the vorticity equations in dimensions two and three
    • [Carpio 1994] A. Carpio, Asymptotic behavior for the vorticity equations in dimensions two and three, Commun. in Partial Differential Equations, 19 (1994), 827–872.
    • (1994) Commun. in Partial Differential Equations , vol.19 , pp. 827-872
    • Carpio, A.1
  • 37
    • 68049136369 scopus 로고    scopus 로고
    • Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics 10
    • [Cazenave 2003] T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics 10, Amer. Math. Soc., Providence RI (2003).
    • (2003) Amer. Math. Soc., Providence RI
    • Cazenave, T.1
  • 40
    • 0032222398 scopus 로고    scopus 로고
    • Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations
    • [Cazenave Weissler 1998a] T. Cazenave and F. B. Weissler, Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z., 228 (1998), 83–120.
    • (1998) Math. Z. , vol.228 , pp. 83-120
    • Cazenave, T.1    Weissler, F.B.2
  • 41
    • 0000177595 scopus 로고    scopus 로고
    • More self-similar solutions of the nonlinear Schrödinger equation
    • [Cazenave Weissler 1998b] T. Cazenave and F. B. Weissler, More self-similar solutions of the nonlinear Schrödinger equation, Nonlin. Diff. Eq. Appl., 5 (1998), 355–365.
    • (1998) Nonlin. Diff. Eq. Appl. , vol.5 , pp. 355-365
    • Cazenave, T.1    Weissler, F.B.2
  • 42
    • 0034375235 scopus 로고    scopus 로고
    • Scattering theory and self-similar solutions for the nonlinear Schrödinger equations
    • [Cazenave Weissler 2000] T. Cazenave and F. B. Weissler, Scattering theory and self-similar solutions for the nonlinear Schrödinger equations, SIAM J. Math Anal., 31 (2000), 625–650.
    • (2000) SIAM J. Math Anal. , vol.31 , pp. 625-650
    • Cazenave, T.1    Weissler, F.B.2
  • 43
    • 34248150423 scopus 로고    scopus 로고
    • Nonexistence of self-similar singularities for the 3D incompressible Euler equations
    • [Chae 2007a] D. Chae, Nonexistence of self-similar singularities for the 3D incompressible Euler equations, Commun. Math. Phys., 273 (2007), 203–215.
    • (2007) Commun. Math. Phys. , vol.273 , pp. 203-215
    • Chae, D.1
  • 44
    • 34248221132 scopus 로고    scopus 로고
    • Nonexistence of asymptotically self-similar singularities in the Euler and the Navier-Stokes equations
    • [Chae 2007b] D. Chae, Nonexistence of asymptotically self-similar singularities in the Euler and the Navier-Stokes equations, Math. Ann., 338 (2007), 435–449.
    • (2007) Math. Ann. , vol.338 , pp. 435-449
    • Chae, D.1
  • 45
    • 36849063807 scopus 로고    scopus 로고
    • Nonexistence of self-similar singularities in the viscous mag-netohydrodynamics with zero resistivity
    • [Chae 2008] D. Chae, Nonexistence of self-similar singularities in the viscous mag-netohydrodynamics with zero resistivity, J. Funct. Anal., 254 (2008), 441–453.
    • (2008) J. Funct. Anal. , vol.254 , pp. 441-453
    • Chae, D.1
  • 46
    • 70350351550 scopus 로고    scopus 로고
    • Nonexistence of self-similar singularities in the ideal magne-tohydrodynamics
    • [Chae 2009] D. Chae, Nonexistence of self-similar singularities in the ideal magne-tohydrodynamics, Arch. Rational Mech. Anal., 194 (2009), 1011–1027.
    • (2009) Arch. Rational Mech. Anal. , vol.194 , pp. 1011-1027
    • Chae, D.1
  • 49
    • 50849145650 scopus 로고
    • Convergence, asymptotic periodicity, and finite-point blow-up in one-dimensional semilinear heat equations
    • [Chen Matano 1989] X.-Y. Chen and H. Matano, Convergence, asymptotic periodicity, and finite-point blow-up in one-dimensional semilinear heat equations, J. Differential Equations, 78 (1989), 160–190.
    • (1989) J. Differential Equations , vol.78 , pp. 160-190
    • Chen, X.-Y.1    Matano, H.2
  • 50
    • 34547255395 scopus 로고    scopus 로고
    • On partial regularity of the borderline solution of semilinear parabolic problems
    • [Chou Du Zheng 2007] K.-S. Chou, S.-Z. Du, and G.-F. Zheng, On partial regularity of the borderline solution of semilinear parabolic problems, Calc. Var and PDEs., 30 (2007), 251–275.
    • (2007) Calc. Var and Pdes. , vol.30 , pp. 251-275
    • Chou, K.-S.1    Du, S.-Z.2    Zheng, G.-F.3
  • 52
    • 0242287337 scopus 로고    scopus 로고
    • R-boundedness, Fourier multipliers, and problems of elliptic and parabolic type
    • [Denk Hieber Prüss 2003] R. Denk, M. Hieber, and J. Prüss, R-boundedness, Fourier multipliers, and problems of elliptic and parabolic type, Mem. Amer. Math. Soc., 166 (2003).
    • (2003) Mem. Amer. Math. Soc. , vol.166
    • Denk, R.1    Hieber, M.2    Prüss, J.3
  • 53
    • 0032115023 scopus 로고    scopus 로고
    • Structure of positive radial solutions to the Haraux-Weissler equation
    • [Dohmen Hirose 1998] C. Dohmen and M. Hirose, Structure of positive radial solutions to the Haraux-Weissler equation, Nonlinear Anal., 33 (1998), 51–69.
    • (1998) Nonlinear Anal. , vol.33 , pp. 51-69
    • Dohmen, C.1    Hirose, M.2
  • 54
    • 0001036795 scopus 로고
    • On rotationally symmetric mean curvature flow
    • [Dziuk Kawohl 1991] G. Dziuk and B. Kawohl, On rotationally symmetric mean curvature flow, J. Differential Equations, 93 (1991), 142–149.
    • (1991) J. Differential Equations , vol.93 , pp. 142-149
    • Dziuk, G.1    Kawohl, B.2
  • 55
    • 0035540757 scopus 로고    scopus 로고
    • A local monotonicity formula for mean curvature flow
    • [Ecker 2001] K. Ecker, A local monotonicity formula for mean curvature flow, Ann. of Math., (2) 154 (2001), 503–525.
    • (2001) Ann. of Math. , vol.154 , Issue.2 , pp. 503-525
    • Ecker, K.1
  • 57
    • 0001821243 scopus 로고
    • Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces
    • [Edmunds Gurka Opic 1995] D. E. Edmunds, P. Gurka, and B. Opic, Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces, Indiana Univ. Math. J., 44 (1995), 19–43.
    • (1995) Indiana Univ. Math. J. , vol.44 , pp. 19-43
    • Edmunds, D.E.1    Gurka, P.2    Opic, B.3
  • 58
    • 0013499323 scopus 로고    scopus 로고
    • Sobolev inequalities of exponential type
    • [Edmunds Hurri-Syrjanen 2001] D. E. Edmunds and R. Hurri-Syrjänen, Sobolev inequalities of exponential type, Israel J. Math., 123 (2001), 61–92.
    • (2001) Israel J. Math. , vol.123 , pp. 61-92
    • Edmunds, D.E.1    Hurri-Syrjänen, R.2
  • 59
    • 58149398261 scopus 로고    scopus 로고
    • The role of self-similarity in singularities of partial differential equations
    • [Eggers Fontelos 2009] J. Eggers and M. A. Fontelos, The role of self-similarity in singularities of partial differential equations, Nonlinearity, 22 (2009), R1–R44.
    • (2009) Nonlinearity , vol.22 , pp. RR1-R44
    • Eggers, J.1    Fontelos, M.A.2
  • 61
    • 0042154193 scopus 로고    scopus 로고
    • 3,∞ solutions of the Navier-Stokes equations and backward uniqueness
    • 3,∞ solutions of the Navier-Stokes equations and backward uniqueness, Russ. Math. Surv., 58(2) (2003), 211–250.
    • (2003) Russ. Math. Surv. , vol.58 , Issue.2 , pp. 211-250
    • Escauriaza, L.1    Seregin, G.2    Sverák, V.3
  • 62
    • 0000457881 scopus 로고
    • Variational problems related to self-similar solutions of the heat equation
    • [Escobedo Kavian 1987] M. Escobedo and O. Kavian, Variational problems related to self-similar solutions of the heat equation, Nonlinear Anal., 11 (1987), 1103–1133.
    • (1987) Nonlinear Anal. , vol.11 , pp. 1103-1133
    • Escobedo, M.1    Kavian, O.2
  • 64
    • 33646917618 scopus 로고
    • A new proof of Moser’s parabolic Harnack inequality using the old idea of Nash
    • [Fabes Stroock 1986] E. B. Fabes and D. W. Stroock, A new proof of Moser’s parabolic Harnack inequality using the old idea of Nash, Arch. Rational Mech. Anal., 96 (1986), 327–338.
    • (1986) Arch. Rational Mech. Anal. , vol.96 , pp. 327-338
    • Fabes, E.B.1    Stroock, D.W.2
  • 65
    • 0002268615 scopus 로고
    • Gaussian upper bounds on fundamental solutions of parabolic equations: The method of Nash
    • [Fabes 1992] E. B. Fabes, Gaussian upper bounds on fundamental solutions of parabolic equations: the method of Nash, Lecture notes in mathematics, 1563 (1992), 1–20.
    • (1992) Lecture Notes in Mathematics , vol.1563 , pp. 1-20
    • Fabes, E.B.1
  • 67
    • 0011234286 scopus 로고    scopus 로고
    • Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
    • [Filippas Herrero Velázquez 2000] S. Filippas, M. A. Herrero, and J. J. L. Velázquez, Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 456 (2000), 2957–2982.
    • (2000) R. Soc. Lond. Proc. Ser. a Math. Phys. Eng. Sci. , vol.456 , pp. 2957-2982
    • Filippas, S.1    Herrero, M.A.2    Velázquez, J.J.L.3
  • 70
    • 84968502599 scopus 로고
    • The asymptotic behavior of gas in an n-dimensional porous medium
    • [Friedman Kamin 1980] A. Friedman and S. Kamin, The asymptotic behavior of gas in an n-dimensional porous medium, Trans. Amer. Math. Soc., 262 (1980), 551–563.
    • (1980) Trans. Amer. Math. Soc. , vol.262 , pp. 551-563
    • Friedman, A.1    Kamin, S.2
  • 75
    • 67649579859 scopus 로고    scopus 로고
    • On the existence of self-similar solutions of the nonlinear Schrödinger equation with power nonlinearity between 1 and 2
    • [Furioli 2001] G. Furioli, On the existence of self-similar solutions of the nonlinear Schrödinger equation with power nonlinearity between 1 and 2, Diff. Integral. Equations, 14 (2001), 1259–1266.
    • (2001) Diff. Integral. Equations , vol.14 , pp. 1259-1266
    • Furioli, G.1
  • 76
    • 0002538288 scopus 로고
    • Ulteriori proprietà di alcune classi di funzioni in più variabili
    • [Gagliardo 1959] E. Gagliardo, Ulteriori proprietà di alcune classi di funzioni in più variabili, Richerche di Mat. Napoli, 8 (1959), 24–51.
    • (1959) Richerche Di Mat. Napoli , vol.8 , pp. 24-51
    • Gagliardo, E.1
  • 78
    • 18244363856 scopus 로고    scopus 로고
    • Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity
    • [Gallagher Gallay 2005] I. Gallagher and Th. Gallay, Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity, Math. Ann., 332 (2005), 287–327.
    • (2005) Math. Ann. , vol.332 , pp. 287-327
    • Gallagher, I.1    Gallay, T.2
  • 79
    • 27744595752 scopus 로고    scopus 로고
    • On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity
    • [Gallagher Gallay Lions 2005] I. Gallagher, Th. Gallay, and P.-L. Lions, On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity, Math. Nachr., 278 (2005), 1665–1672.
    • (2005) Math. Nachr. , vol.278 , pp. 1665-1672
    • Gallagher, I.1    Gallay, T.2    Lions, P.-L.3
  • 81
    • 21244476087 scopus 로고    scopus 로고
    • Global Stability of vortex solutions of the two dimensional Navier-Stokes equation
    • [Gallay Wayne 2005] Th. Gallay and C. E. Wayne, Global Stability of vortex solutions of the two dimensional Navier-Stokes equation, Commun. Math. Phys., 255 (2005), 97–129.
    • (2005) Commun. Math. Phys. , vol.255 , pp. 97-129
    • Gallay, T.1    Wayne, C.E.2
  • 82
    • 30144432938 scopus 로고    scopus 로고
    • Three-dimensional stability of Burgers vortices: The low Reynolds number case
    • [Gallay Wayne 2006] Th. Gallay and C. E. Wayne, Three-dimensional stability of Burgers vortices: the low Reynolds number case, Physica D, 213 (2006), 164–180.
    • (2006) Physica D , vol.213 , pp. 164-180
    • Gallay, T.1    Wayne, C.E.2
  • 83
    • 34250185708 scopus 로고    scopus 로고
    • Existence and stability of asymmetric Burgers vortices
    • [Gallay Wayne 2007] Th. Gallay and C. E. Wayne, Existence and stability of asymmetric Burgers vortices, J. Math. Fluid. Mech., 9 (2007), 243–261.
    • (2007) J. Math. Fluid. Mech. , vol.9 , pp. 243-261
    • Gallay, T.1    Wayne, C.E.2
  • 85
    • 46149140458 scopus 로고
    • p and regularity of weak solutions of the Navier-Stokes system
    • p and regularity of weak solutions of the Navier-Stokes system, J. Differential Equations, 61 (1986), 186–212.
    • (1986) J. Differential Equations , vol.61 , pp. 186-212
    • Giga, Y.1
  • 86
    • 0038417900 scopus 로고    scopus 로고
    • A level set method for surface evolution equations
    • Translated from the Japanese original in Sûgaku, 47 (1995), 321–340
    • [Giga 1995] Y. Giga, A level set method for surface evolution equations, Sugaku Expositions, 10 (1997), 217–241. Translated from the Japanese original in Sûgaku, 47 (1995), 321–340.
    • (1997) Sugaku Expositions , vol.10 , pp. 217-241
    • Giga, Y.1
  • 90
    • 0001226214 scopus 로고
    • Large time behavior of the vorticity of two dimensional viscous flow and its application to vortex formation
    • [Giga Kambe 1988] Y. Giga and T. Kambe, Large time behavior of the vorticity of two dimensional viscous flow and its application to vortex formation, Comm. Math. Phys., 117 (1988), 549–568.
    • (1988) Comm. Math. Phys. , vol.117 , pp. 549-568
    • Giga, Y.1    Kambe, T.2
  • 91
    • 84990616610 scopus 로고
    • Asymptotically self-similar blow-up of semilinear heat equations
    • [Giga Kohn 1985] Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math., 38 (1985), 297–319.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 297-319
    • Giga, Y.1    Kohn, R.V.2
  • 92
    • 0000332576 scopus 로고
    • Characterizing blowup using similarity variables
    • [Giga Kohn 1987] Y. Giga and R. V. Kohn, Characterizing blowup using similarity variables, Indiana Univ. Math. J., 36 (1987), 1–40.
    • (1987) Indiana Univ. Math. J. , vol.36 , pp. 1-40
    • Giga, Y.1    Kohn, R.V.2
  • 93
    • 84990575181 scopus 로고
    • Nondegeneracy of blowup for semilinear heat equations
    • [Giga Kohn 1989] Y. Giga and R. V. Kohn, Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math., 42 (1989), 845–884.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 845-884
    • Giga, Y.1    Kohn, R.V.2
  • 94
    • 3042688935 scopus 로고    scopus 로고
    • Blow-up rate for semilinear heat equations with subcritical nonlinearity
    • [Giga Matsui Sasayama 2004a] Y. Giga, S. Matsui, and S. Sasayama, Blow-up rate for semilinear heat equations with subcritical nonlinearity, Indiana Univ. Math. J., 53 (2004), 483–514.
    • (2004) Indiana Univ. Math. J. , vol.53 , pp. 483-514
    • Giga, Y.1    Matsui, S.2    Sasayama, S.3
  • 95
    • 4744344778 scopus 로고    scopus 로고
    • On blow-up rate for sign-changing solutions in a convex domain
    • [Giga Matsui Sasayama 2004b] Y. Giga, S. Matsui, and S. Sasayama, On blow-up rate for sign-changing solutions in a convex domain, Math. Methods Appl. Sci., 27 (2004), 1771–1782.
    • (2004) Math. Methods Appl. Sci. , vol.27 , pp. 1771-1782
    • Giga, Y.1    Matsui, S.2    Sasayama, S.3
  • 96
    • 84950020948 scopus 로고
    • 3 with measures as initial vorticity and Morrey spaces, Commun
    • 3 with measures as initial vorticity and Morrey spaces, Commun. in Partial Differential Equations, 14 (1989), 577–618.
    • (1989) Partial Differential Equations , vol.14 , pp. 577-618
    • Giga, Y.1    Miyakawa, T.2
  • 97
    • 0001300372 scopus 로고
    • Two dimensional Navier-Stokes flow with measures as initial vorticity
    • [Giga Miyakawa Osada 1988] Y. Giga, T. Miyakawa and H. Osada, Two dimensional Navier-Stokes flow with measures as initial vorticity, Arch. Rational Mech. Anal., 104 (1988), 223–250.
    • (1988) Arch. Rational Mech. Anal. , vol.104 , pp. 223-250
    • Giga, Y.1    Miyakawa, T.2    Osada, H.3
  • 101
    • 33749632825 scopus 로고    scopus 로고
    • Self-similar solutions to the isothermal compressible Navier-Stokes equations
    • [Guo Jiang 2006] Z. Guo and S. Jiang, Self-similar solutions to the isothermal compressible Navier-Stokes equations, IMA Journal of Applied Mathematics, 71 (2006), 658–669.
    • (2006) IMA Journal of Applied Mathematics , vol.71 , pp. 658-669
    • Guo, Z.1    Jiang, S.2
  • 102
    • 0001409903 scopus 로고
    • Nonuniqueness for a semilinear initial value problem
    • [Haraux Weissler 1982] A. Haraux and F. B. Weissler, Nonuniqueness for a semilinear initial value problem, Indiana Univ. Math. J., 31 (1982), 167–189.
    • (1982) Indiana Univ. Math. J. , vol.31 , pp. 167-189
    • Haraux, A.1    Weissler, F.B.2
  • 103
    • 85011578583 scopus 로고
    • Blow-up behaviour of one-dimensional semilinear parabolic equations
    • [Herrero Velázquez 1993] M. A. Herrero and J. J. L. Velázquez, Blow-up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poincaré, 10 (1993), 131–189.
    • (1993) Ann. Inst. Henri Poincaré , vol.10 , pp. 131-189
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 104
    • 0000172301 scopus 로고
    • Explosion de solutions d’équations paraboliques semilinéaires supercritiques
    • [Herrero Velázquez 1994] M. A. Herrero and J. J. L. Velázquez, Explosion de solutions d’équations paraboliques semilinéaires supercritiques, C. R. Acad. Sci. Paris Sér.I Math., 319 (1994), 141–145.
    • (1994) C. R. Acad. Sci. Paris Sér.I Math. , vol.319 , pp. 141-145
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 106
    • 0012485651 scopus 로고    scopus 로고
    • The Herbert Amann anniversary volume (eds. J. Escher et al.), Progress in Nonlinear Differential Equations and Applications, Birkhäuser, Basel
    • [Hieber 1999] M. Hieber, Operator valued Fourier multipliers, Topics in nonlinear analysis, The Herbert Amann anniversary volume (eds. J. Escher et al.), Progress in Nonlinear Differential Equations and Applications, 35, Birkhäuser, Basel (1999), 363–380.
    • (1999) Operator Valued Fourier Multipliers, Topics in Nonlinear Analysis , vol.35 , pp. 363-380
    • Hieber, M.1
  • 107
    • 85045430653 scopus 로고    scopus 로고
    • Mathematical analysis of the equations for incompressible viscous fluid around a rotating obstacle
    • (in Japanese)
    • [Hishida 2008] T. Hishida, Mathematical analysis of the equations for incompressible viscous fluid around a rotating obstacle, Sûgaku 60 (2008), 68–94 (in Japanese).
    • (2008) Sûgaku , vol.60 , pp. 68-94
    • Hishida, T.1
  • 108
    • 84972527004 scopus 로고
    • Asymptotic behavior for singularities of the mean curvature flow
    • [Huisken 1990] G. Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geometry, 31(1990), 285–299.
    • (1990) J. Differential Geometry , vol.31 , pp. 285-299
    • Huisken, G.1
  • 109
    • 0002977655 scopus 로고
    • Local and global behaviour of hypersurfaces moving by mean curvature
    • Amer. Math. Soc
    • [Huisken 1993] G. Huisken, Local and global behaviour of hypersurfaces moving by mean curvature, Proc. Sym. Pure Math., 54 (1993) Part I, 175–191 Amer. Math. Soc.
    • (1993) Proc. Sym. Pure Math. , vol.54 , pp. 175-191
    • Huisken, G.1
  • 111
    • 2342493679 scopus 로고    scopus 로고
    • American Math. Soc. (2000). In translated from the 1997 Japanese original published by Iwanami, Tokyo
    • [Ikawa 1997] M. Ikawa, Hyperbolic Partial Differential Equations and Wave Phenomena, American Math. Soc. (2000). In translated from the 1997 Japanese original published by Iwanami, Tokyo (1997).
    • (1997) Hyperbolic Partial Differential Equations and Wave Phenomena
    • Ikawa, M.1
  • 115
    • 78951494685 scopus 로고
    • On blowing up of solutions of semilinear partial differential equations of parabolic type
    • (in Japanese)
    • [Ito 1966] S. Itô, On blowing up of solutions of semilinear partial differential equations of parabolic type, Sûgaku, 18 (1966), 44–47 (in Japanese).
    • (1966) Sûgaku , vol.18 , pp. 44-47
    • Itô, S.1
  • 116
    • 85045454556 scopus 로고
    • Translated from the 1979 Japanese original published by Kinokuniya, Tokyo
    • [Ito 1979] S. Itô, Diffusion equations, Amer. Math. Soc. (1992). Translated from the 1979 Japanese original published by Kinokuniya, Tokyo (1979).
    • (1992) Diffusion Equations, Amer. Math. Soc.
    • Itô, S.1
  • 117
    • 0042938494 scopus 로고
    • On blow-up of positive solutions of semilinear parabolic equations
    • [Ito 1990] S. Itô, On blow-up of positive solutions of semilinear parabolic equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 37 (1990), 527–536.
    • (1990) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.37 , pp. 527-536
    • Itô, S.1
  • 119
    • 84980082306 scopus 로고
    • On functions of bounded mean oscillation
    • [John Nirenberg 1961] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14 (1961), 415–426.
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 415-426
    • John, F.1    Nirenberg, L.2
  • 120
    • 0003905011 scopus 로고    scopus 로고
    • third edition, Springer Berlin
    • [Jost 2005] J. Jost, Postmodern analysis, third edition, Springer Berlin (2005).
    • (2005) Postmodern Analysis
    • Jost, J.1
  • 122
    • 0020719966 scopus 로고
    • A class of exact solutions of two-dimensional viscous flow
    • [Kambe 1983] T. Kambe, A class of exact solutions of two-dimensional viscous flow, J. Phys. Soc. Jpn., 52 (1983), 834–841.
    • (1983) J. Phys. Soc. Jpn. , vol.52 , pp. 834-841
    • Kambe, T.1
  • 123
    • 0021214543 scopus 로고
    • Axisymmetric vortex solution of Navier-Stokes equation
    • [Kambe 1984] T. Kambe, Axisymmetric vortex solution of Navier-Stokes equation, J. Phys. Soc. Jpn., 53 (1984), 13–15.
    • (1984) J. Phys. Soc. Jpn. , vol.53 , pp. 13-15
    • Kambe, T.1
  • 124
    • 85045423697 scopus 로고    scopus 로고
    • Introduction to partial differential equations
    • (in Japanese)
    • [Kaneko 1998] A. Kaneko, Introduction to partial differential equations, U. of Tokyo Press (1998) (in Japanese).
    • (1998) U. of Tokyo Press
    • Kaneko, A.1
  • 125
    • 84980080195 scopus 로고
    • On the growth of solutions of quasi-linear parabolic equations
    • [Kaplan 1963] S. Kaplan, On the growth of solutions of quasi-linear parabolic equations, Comm. Pure Appl. Math., 16 (1963) 305–330.
    • (1963) Comm. Pure Appl. Math. , vol.16 , pp. 305-330
    • Kaplan, S.1
  • 126
    • 0002362136 scopus 로고
    • On the Cauchy problem for the (Generalized) Korteweg-de Vries equation
    • Academic Press, New York
    • [Kato 1983] T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, “Studies in Appl. Math. Advances in Math. Suppl. Studies,” vol. 8, pp. 93–128, Academic Press, New York (1983).
    • (1983) Studies in Appl. Math. Advances in Math. Suppl. Studies , vol.8 , pp. 93-128
    • Kato, T.1
  • 127
    • 84972545764 scopus 로고
    • 2 with a measure as the initial vorticity
    • 2 with a measure as the initial vorticity, Diff. Integral Equations, 7 (1994), 949–966.
    • (1994) Diff. Integral Equations , vol.7 , pp. 949-966
    • Kato, T.1
  • 128
    • 67649582805 scopus 로고    scopus 로고
    • On well-posedness
    • (in Japanese)
    • [Kato 1996] T. Kato, On well-posedness, Sûgaku, 48 (1996), 298–300 (in Japanese).
    • (1996) Sûgaku , vol.48 , pp. 298-300
    • Kato, T.1
  • 129
    • 0001464559 scopus 로고
    • On the nonstationary Navier-Stokes system
    • [Kato Fujita 1962] T. Kato and H. Fujita, On the nonstationary Navier-Stokes system, Rend. Sem. Mat. Univ Padova, 32 (1962), 243–260.
    • (1962) Rend. Sem. Mat. Univ Padova , vol.32 , pp. 243-260
    • Kato, T.1    Fujita, H.2
  • 130
    • 0030363289 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity
    • [Kawanago 1996] T. Kawanago, Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), 1–15.
    • (1996) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.13 , pp. 1-15
    • Kawanago, T.1
  • 131
    • 0001182260 scopus 로고
    • Spatiotemporal intermittency and instability of a forced turbulence
    • [Kida Ohkitani 1992] S. Kida and K. Ohkitani, Spatiotemporal intermittency and instability of a forced turbulence, Phys. Fluids A, 4(5) (1992), 1018–1027.
    • (1992) Phys. Fluids A , vol.4 , Issue.5 , pp. 1018-1027
    • Kida, S.1    Ohkitani, K.2
  • 133
    • 85035259927 scopus 로고
    • Iwanami, Tokyo, (in Japanese)
    • [Komatsu 1978] H. Komatsu, Fourier analysis, Iwanami, Tokyo (1978) (in Japanese).
    • (1978) Fourier Analysis
    • Komatsu, H.1
  • 134
    • 85045427568 scopus 로고    scopus 로고
    • On equations of viscous incompressible flow, surikagaku
    • (in Japanese)
    • [Kozono 1997] H. Kozono, On equations of viscous incompressible flow, surikagaku, November (1999), 9–14 (in Japanese).
    • (1999) November , pp. 9-14
    • Kozono, H.1
  • 135
    • 0043106637 scopus 로고    scopus 로고
    • Uniqueness and regularity of weak solutions to the Navier-Stokes equations
    • (Tsukuba 1996), Lecture Notes Numer. Appl. Anal 10,Kinokuniya, Tokyo
    • [Kozono 1998] H. Kozono, Uniqueness and regularity of weak solutions to the Navier-Stokes equations, Recent Topics on Mathematical Theory of Viscous Incompressible Fluid (Tsukuba 1996), Lecture Notes Numer. Appl. Anal 10, Kinokuniya, Tokyo (1998), 161–208.
    • (1998) Recent Topics on Mathematical Theory of Viscous Incompressible Fluid , pp. 161-208
    • Kozono, H.1
  • 136
    • 85045459764 scopus 로고    scopus 로고
    • The Navier-Stokes equations
    • (in Japanese)
    • [Kozono 2002] H. Kozono, The Navier-Stokes equations, Sûgaku, 54 (2002), 178–202 (in Japanese).
    • (2002) Sûgaku , vol.54 , pp. 178-202
    • Kozono, H.1
  • 137
    • 0012945781 scopus 로고    scopus 로고
    • The critical Sobolev inequalities in Besov spaces and regularity criterion to some semilinear evolution equations
    • [Kozono Ogawa Taniuchi 2002] H. Kozono, T. Ogawa, and Y. Taniuchi, The critical Sobolev inequalities in Besov spaces and regularity criterion to some semilinear evolution equations, Math. Z., 242 (2002), 251–278.
    • (2002) Math. Z. , vol.242 , pp. 251-278
    • Kozono, H.1    Ogawa, T.2    Taniuchi, Y.3
  • 138
    • 0001532575 scopus 로고    scopus 로고
    • Remark on uniqueness of weak solutions to the Navier-Stokes equations
    • [Kozono Sohr 1996] H. Kozono and H. Sohr, Remark on uniqueness of weak solutions to the Navier-Stokes equations, Analysis 16 (1996), 255–271.
    • (1996) Analysis , vol.16 , pp. 255-271
    • Kozono, H.1    Sohr, H.2
  • 139
    • 0000946209 scopus 로고
    • Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data, Commun
    • [Kozono Yamazaki 1994] H. Kozono and M. Yamazaki, Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data, Commun. in Partial Differential Equations, 19 (1994), 959–1014.
    • (1994) Partial Differential Equations , vol.19 , pp. 959-1014
    • Kozono, H.1    Yamazaki, M.2
  • 140
    • 0039223237 scopus 로고
    • The stability of small stationary solutions in Morrey spaces of the Navier-Stokes equation
    • [Kozono Yamazaki 1995] H. Kozono and M. Yamazaki, The stability of small stationary solutions in Morrey spaces of the Navier-Stokes equation, Indiana Univ. Math. J., 44 (1995), 1307–1336.
    • (1995) Indiana Univ. Math. J. , vol.44 , pp. 1307-1336
    • Kozono, H.1    Yamazaki, M.2
  • 142
    • 0004021335 scopus 로고
    • Kyoritsu, Tokyo, Japan, (in Japanese)
    • [Kuroda 1980] S. Kuroda, Functional Analysis, Kyoritsu, Tokyo, Japan, (1980) (in Japanese).
    • (1980) Functional Analysis
    • Kuroda, S.1
  • 143
    • 0003223550 scopus 로고
    • Linear and quasilinear equations of parabolic type, Translation of Math. Monographs
    • [Ladyženskaja Solonnikov Ural’ceva 1968] O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural’ceva, Linear and quasilinear equations of parabolic type, Translation of Math. Monographs 23, Amer. Math. Soc., Providence (1968).
    • (1968) Amer. Math. Soc., Providence , vol.23
    • Ladyženskaja, O.A.1    Solonnikov, V.A.2    Ural’Ceva, N.N.3
  • 145
    • 36549046605 scopus 로고    scopus 로고
    • Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption
    • [Laurençot Vázquez 2007] P. Laurençot and J. L. Vázquez, Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption, J. Dynam. Differential Equations, 19 (2007), 985–1005.
    • (2007) J. Dynam. Differential Equations , vol.19 , pp. 985-1005
    • Laurençot, P.1    Vázquez, J.L.2
  • 146
    • 0031522024 scopus 로고    scopus 로고
    • Stochastic cascades and 3-dimensional Navier-Stokes equations
    • [LeJan Sznitman 1997] Y. Le Jan and A.-S. Sznitman, Stochastic cascades and 3-dimensional Navier-Stokes equations, Probab. Theory Related Fields, 109 (3) (1997), 343–366.
    • (1997) Probab. Theory Related Fields , vol.109 , Issue.3 , pp. 343-366
    • Le Jan, Y.1    Sznitman, A.-S.2
  • 147
    • 0039162116 scopus 로고
    • Countable spectrum of the eigenfunctions of the nonlinear heat equation with distributed parameters
    • [Lepin 1988] L. A. Lepin, Countable spectrum of the eigenfunctions of the nonlinear heat equation with distributed parameters, Differ. Uravn., 24 (1988), 1226–1234
    • (1988) Differ. Uravn. , vol.24 , pp. 1226-1234
    • Lepin, L.A.1
  • 148
    • 0013065771 scopus 로고
    • English translation
    • English translation; Differ. Equ., 24 (1988), 799–805.
    • (1988) Differ. Equ. , vol.24 , pp. 799-805
  • 149
    • 0012859161 scopus 로고
    • Self-similar solutions of a semilinear heat equation
    • (in Russian)
    • [Lepin 1990] L. A. Lepin, Self-similar solutions of a semilinear heat equation, Mat. Model., 2 (1990), 63–74 (in Russian).
    • (1990) Mat. Model. , vol.2 , pp. 63-74
    • Lepin, L.A.1
  • 150
    • 0003068173 scopus 로고
    • Étude de diverses équations intégrales non linéaires et de quelque problèmes que pose l’ Hydrodynamique
    • [Leray 1933] J. Leray, Étude de diverses équations intégrales non linéaires et de quelque problèmes que pose l’ Hydrodynamique, J. Math. Pures Appl., 12 (1933), 1–82.
    • (1933) J. Math. Pures Appl. , vol.12 , pp. 1-82
    • Leray, J.1
  • 151
    • 0000221349 scopus 로고
    • Essai sur les mouvements plans d’un liquide visqueux que limitent des parois
    • [Leray 1934a] J. Leray, Essai sur les mouvements plans d’un liquide visqueux que limitent des parois, J. Math. Pures Appl., 13 (1934), 331–418.
    • (1934) J. Math. Pures Appl. , vol.13 , pp. 331-418
    • Leray, J.1
  • 152
    • 51249193194 scopus 로고
    • Sur le mouvement d’un liquids visqueux emplissant l’espace
    • [Leray 1934b] J. Leray, Sur le mouvement d’un liquids visqueux emplissant l’espace, Acta Math., 63(1934), 193–248.
    • (1934) Acta Math. , vol.63 , pp. 193-248
    • Leray, J.1
  • 153
    • 0025442951 scopus 로고
    • The role of critical exponents in blow-up theorems
    • [Levine 1990] H. A. Levine, The role of critical exponents in blow-up theorems, SIAM Review, 32 (1990), 262–288.
    • (1990) SIAM Review , vol.32 , pp. 262-288
    • Levine, H.A.1
  • 156
    • 0034287964 scopus 로고    scopus 로고
    • Estimates for fundamental solutions of second-order parabolic equations
    • [Liskevich Samenov 2000] V. Liskevich and Y. A. Samenov, Estimates for fundamental solutions of second-order parabolic equations, J. London Math. Soc., 62 (2) (2000), 521–543.
    • (2000) J. London Math. Soc. , vol.62 , Issue.2 , pp. 521-543
    • Liskevich, V.1    Samenov, Y.A.2
  • 157
    • 1542718390 scopus 로고    scopus 로고
    • Extra regularity for parabolic equations with drift terms
    • [Liskevich Zhang 2004] V. Liskevich and Q. S. Zhang, Extra regularity for parabolic equations with drift terms, Manuscripta Math., 113 no. 2 (2004), 191–209.
    • (2004) Manuscripta Math. , vol.113 , Issue.2 , pp. 191-209
    • Liskevich, V.1    Zhang, Q.S.2
  • 159
    • 0344769882 scopus 로고
    • Strained spiral vortex model for turbulent fine structure
    • [Lundgren 1982] T. S. Lundgren, Strained spiral vortex model for turbulent fine structure, Phys. Fluids., 25 (1982), 2193–2203.
    • (1982) Phys. Fluids. , vol.25 , pp. 2193-2203
    • Lundgren, T.S.1
  • 160
    • 40249111818 scopus 로고    scopus 로고
    • On spatial decay estimates for derivatives of vor-ticities with application to large time behavior of the two-dimensional Navier-Stokes flow
    • [Maekawa 2008a] Y. Maekawa, On spatial decay estimates for derivatives of vor-ticities with application to large time behavior of the two-dimensional Navier-Stokes flow, J. Math. Fluid Mech., 10 (2008), 89–105.
    • (2008) J. Math. Fluid Mech. , vol.10 , pp. 89-105
    • Maekawa, Y.1
  • 161
    • 43749091265 scopus 로고    scopus 로고
    • A lower bound for fundamental solutions of the heat convection equations
    • [Maekawa 2008b] Y. Maekawa, A lower bound for fundamental solutions of the heat convection equations, Arch. Rational Mech. Anal., 189 (2008), 45–58.
    • (2008) Arch. Rational Mech. Anal. , vol.189 , pp. 45-58
    • Maekawa, Y.1
  • 162
    • 52749099311 scopus 로고    scopus 로고
    • On the existence of Burgers vortices for high Reynolds numbers
    • [Maekawa 2009a] Y. Maekawa, On the existence of Burgers vortices for high Reynolds numbers, J. Math. Anal. Appl., 349 (2009), 181–200.
    • (2009) J. Math. Anal. Appl. , vol.349 , pp. 181-200
    • Maekawa, Y.1
  • 163
    • 67650077663 scopus 로고    scopus 로고
    • Existence of asymmetric Burgers vortices and their asymptotic behavior at large circulations
    • [Maekawa 2009b] Y. Maekawa, Existence of asymmetric Burgers vortices and their asymptotic behavior at large circulations, Math. Model., Meth. in Appl. Sci., 19 (2009), 669–705.
    • (2009) Math. Model., Meth. in Appl. Sci. , vol.19 , pp. 669-705
    • Maekawa, Y.1
  • 164
    • 0040111702 scopus 로고    scopus 로고
    • On possible singular solutions to the Navier-Stokes equations
    • [Málek Nečas Pokorný Schonbek 1999] J. Málek, J. Nečas, M. Pokorný, and M. Schonbek, On possible singular solutions to the Navier-Stokes equations, Math. Nachr., 199 (1999), 97–114.
    • (1999) Math. Nachr. , vol.199 , pp. 97-114
    • Málek, J.1    Nečas, J.2    Pokorný, M.3    Schonbek, M.4
  • 165
    • 33845223403 scopus 로고    scopus 로고
    • Some interpolating inequalities involving Stokes operator and first order derivatives
    • [Maremonti 1998] P. Maremonti, Some interpolating inequalities involving Stokes operator and first order derivatives, Annali di Matematica Pura ed Applicata, 175 (1998), 59–91.
    • (1998) Annali Di Matematica Pura Ed Applicata , vol.175 , pp. 59-91
    • Maremonti, P.1
  • 166
    • 0036016142 scopus 로고    scopus 로고
    • 2 -critical generalized KdV equation
    • 2 -critical generalized KdV equation, J. Amer. Math. Soc., 15 (2002), 617–664.
    • (2002) J. Amer. Math. Soc. , vol.15 , pp. 617-664
    • Martel, Y.1    Merle, F.2
  • 168
    • 0011564526 scopus 로고
    • Nonlinear Diffusion Equations and Their Equilibrium States IIW.-M. Ni et alSpringer
    • 1, “Nonlinear Diffusion Equations and Their Equilibrium States II” (ed. W.-M. Ni et al.), Springer (1986), 139–162.
    • (1986) 1 , pp. 139-162
    • Matano, H.1
  • 170
    • 7044224827 scopus 로고    scopus 로고
    • On nonexistence of type II blowup for a supercritical nonlinear heat equation
    • [Matano Merle 2004] H. Matano and F. Merle, On nonexistence of type II blowup for a supercritical nonlinear heat equation, Comm. Pure Appl. Math., 57 (2004), 1494–1541.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 1494-1541
    • Matano, H.1    Merle, F.2
  • 171
    • 43749103408 scopus 로고    scopus 로고
    • Remark on fundamental solution for vorticity equation of two dimensional Navier-Stokes flows
    • [Matsui Tokuno 1997] S. Matsui and S. Tokuno, Remark on fundamental solution for vorticity equation of two dimensional Navier-Stokes flows, Hokkaido Math. J., 26 (1997), 529–539.
    • (1997) Hokkaido Math. J. , vol.26 , pp. 529-539
    • Matsui, S.1    Tokuno, S.2
  • 173
    • 0032338170 scopus 로고    scopus 로고
    • Optimal estimates for blowup rate and behavior for nonlinear heat equations
    • [Merle Zaag 1998] F. Merle and H. Zaag, Optimal estimates for blowup rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math., 51 (1998), 139–196.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 139-196
    • Merle, F.1    Zaag, H.2
  • 175
    • 34047212131 scopus 로고    scopus 로고
    • Self-similar solutions for nonlinear Schrödinger equations
    • [Miao Zhang Zhang 2003] C. Miao, B. Zhang, and X. Zhang, Self-similar solutions for nonlinear Schrödinger equations, Methods Appl. Anal., 10 (2003), 119–136.
    • (2003) Methods Appl. Anal. , vol.10 , pp. 119-136
    • Miao, C.1    Zhang, B.2    Zhang, X.3
  • 176
    • 0035607661 scopus 로고    scopus 로고
    • Nonexistence of singular pseudo-self-similar solutions of the Navier-Stokes system
    • [Miller O’Leary Schonbek 2001] J. R. Miller, M. O’Leary, and M. Schonbek, Nonexistence of singular pseudo-self-similar solutions of the Navier-Stokes system, Math. Ann., 319 (2001), 809–815.
    • (2001) Math. Ann. , vol.319 , pp. 809-815
    • Miller, J.R.1    O’Leary, M.2    Schonbek, M.3
  • 177
    • 0001781565 scopus 로고    scopus 로고
    • Hardy spaces of solenoidal vector fields, with applications to the Navier-Stokes equations
    • [Miyakawa 1996] T. Miyakawa, Hardy spaces of solenoidal vector fields, with applications to the Navier-Stokes equations, Kyushu J. Math., 50 (1996), 1–64.
    • (1996) Kyushu J. Math. , vol.50 , pp. 1-64
    • Miyakawa, T.1
  • 180
    • 59849107682 scopus 로고    scopus 로고
    • Type-II blowup for a semilinear heat equation
    • [Mizoguchi 2004a] N. Mizoguchi, Type-II blowup for a semilinear heat equation, Adv. Differential Equations, 9 (2004), 1279–1316.
    • (2004) Adv. Differential Equations , vol.9 , pp. 1279-1316
    • Mizoguchi, N.1
  • 181
    • 4344718737 scopus 로고    scopus 로고
    • Blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity
    • [Mizoguchi 2004b] N. Mizoguchi, Blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity, J. Differential Equations, 205 (2004), 298–328.
    • (2004) J. Differential Equations , vol.205 , pp. 298-328
    • Mizoguchi, N.1
  • 182
    • 0039484044 scopus 로고    scopus 로고
    • Exponential integrability for Riesz potentials of functions in Orlicz classes
    • [Mizuta Shimomura 1998] Y. Mizuta and T. Shimomura, Exponential integrability for Riesz potentials of functions in Orlicz classes, Hiroshima Math. J., 28 (1998), 355–371.
    • (1998) Hiroshima Math. J. , vol.28 , pp. 355-371
    • Mizuta, Y.1    Shimomura, T.2
  • 183
    • 0028160302 scopus 로고
    • Stretched vortices—the sinews of turbulence; large-Reynolds-number asymptotics
    • [Moffatt Kida Ohkitani 1994] H. K. Moffatt, S. Kida, and K. Ohkitani, Stretched vortices—the sinews of turbulence; large-Reynolds-number asymptotics, J. Fluid Mech., 259 (1994), 241–264.
    • (1994) J. Fluid Mech. , vol.259 , pp. 241-264
    • Moffatt, H.K.1    Kida, S.2    Ohkitani, K.3
  • 184
    • 0344064887 scopus 로고    scopus 로고
    • On the Cauchy problem of the generalized Korteweg-de Vries equations
    • [Molinet Ribaud 2003] L. Molinet and F. Ribaud, On the Cauchy problem of the generalized Korteweg-de Vries equations, Comm. Partial Differential Equations, 28 (2003), 2065–2091.
    • (2003) Comm. Partial Differential Equations , vol.28 , pp. 2065-2091
    • Molinet, L.1    Ribaud, F.2
  • 185
    • 0003418230 scopus 로고
    • third edition, Academic Press Inc., San Diego CA, (2000), first edition
    • [Morgan 1991] F. Morgan, Geometric Measure Theory, A beginner’s guide, third edition, Academic Press Inc., San Diego CA, (2000), first edition, (1991).
    • (1991) Geometric Measure Theory, a beginner’s Guide
    • Morgan, F.1
  • 186
    • 0001173833 scopus 로고
    • A sharp form of an inequality by N. Trudinger, Indiana Univ
    • [Moser 1970] J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J., 20 (1970), 1077–1092.
    • (1970) Math. J. , vol.20 , pp. 1077-1092
    • Moser, J.1
  • 189
    • 0001205112 scopus 로고    scopus 로고
    • Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis
    • [Nagai Senba Yoshida 1997] T. Nagai, T. Senba, and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcialaj Ekvacioj, 40 (1997), 411–433.
    • (1997) Funkcialaj Ekvacioj , vol.40 , pp. 411-433
    • Nagai, T.1    Senba, T.2    Yoshida, K.3
  • 190
    • 2442582442 scopus 로고    scopus 로고
    • Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data
    • [Naito 2004] Y. Naito, Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data, Math. Ann., 329 (2004), 161–196.
    • (2004) Math. Ann. , vol.329 , pp. 161-196
    • Naito, Y.1
  • 191
    • 33748307372 scopus 로고    scopus 로고
    • An ODE approach to the multiplicity of self-similar solutions for semilinear heat equations
    • [Naito 2006] Y. Naito, An ODE approach to the multiplicity of self-similar solutions for semilinear heat equations, Proc. Roy. Soc. Edinburgh Sect. A., 136 (2006), 807–835.
    • (2006) Proc. Roy. Soc. Edinburgh Sect. A. , vol.136 , pp. 807-835
    • Naito, Y.1
  • 192
    • 49549085530 scopus 로고    scopus 로고
    • Self-similar solutions for a semilinear heat equation with critical Sobolev exponent
    • [Naito 2008] Y. Naito, Self-similar solutions for a semilinear heat equation with critical Sobolev exponent, Indiana Univ. Math. J., 57 (2008), 1283–1315.
    • (2008) Indiana Univ. Math. J. , vol.57 , pp. 1283-1315
    • Naito, Y.1
  • 194
    • 0010852697 scopus 로고    scopus 로고
    • Radial symmetry of self-similar solutions for semilinear heat equations
    • [Naito Suzuki 2000] Y. Naito and T. Suzuki, Radial symmetry of self-similar solutions for semilinear heat equations, J. Differential Equations, 163 (2000), 407–428.
    • (2000) J. Differential Equations , vol.163 , pp. 407-428
    • Naito, Y.1    Suzuki, T.2
  • 195
    • 33750177589 scopus 로고    scopus 로고
    • Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity
    • [Naito Suzuki 2007] Y. Naito and T. Suzuki, Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity, J. Differential Equations, 232 (2007), 176–211.
    • (2007) J. Differential Equations , vol.232 , pp. 176-211
    • Naito, Y.1    Suzuki, T.2
  • 196
    • 0001680091 scopus 로고
    • Continuity of solutions of parabolic and elliptic equations
    • [Nash 1958] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80 (1958), 931–954.
    • (1958) Amer. J. Math. , vol.80 , pp. 931-954
    • Nash, J.1
  • 197
    • 0001654863 scopus 로고    scopus 로고
    • On Leray’s self-similar solutions of the Navier-Stokes equations
    • ◦ Šverák 1996] J. Nečas, M. Ružička and V. Šverák, On Leray’s self-similar solutions of the Navier-Stokes equations, Acta Math., 176 (1996), 283–294.
    • (1996) Acta Math. , vol.176 , pp. 283-294
    • Nečas, J.1    Ružička, M.2    Šverák, V.3
  • 198
    • 0000973918 scopus 로고
    • On elliptic partial differential equations
    • [Nirenberg 1959] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (Ser. III), 13 (1959), 115–162.
    • (1959) Ann. Scuola Norm. Sup. Pisa (Ser. III) , vol.13 , pp. 115-162
    • Nirenberg, L.1
  • 199
    • 85045480759 scopus 로고    scopus 로고
    • Far-from-equlibrium Dynamics
    • Translated from the 1999 Japanese original published by Iwanami, Tokyo
    • [Nishiura 1999] Y. Nishiura, Far-from-equlibrium Dynamics, Amer. Math. Soc. (2002). Translated from the 1999 Japanese original published by Iwanami, Tokyo.
    • (2002) Amer. Math. Soc.
    • Nishiura, Y.1
  • 200
    • 0242679760 scopus 로고    scopus 로고
    • Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow
    • [Ogawa 2003] T. Ogawa, Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow, SIAM J. Math. Anal., 34 (2003), 1318–1330.
    • (2003) SIAM J. Math. Anal. , vol.34 , pp. 1318-1330
    • Ogawa, T.1
  • 201
    • 1942539813 scopus 로고    scopus 로고
    • The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces
    • [Ogawa Taniuchi 2004] T. Ogawa, Y. Taniuchi, The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces, Tohoku Math. J., 56 (2004), 65–77.
    • (2004) Tohoku Math. J. , vol.56 , pp. 65-77
    • Ogawa, T.1    Taniuchi, Y.2
  • 202
    • 85045451685 scopus 로고    scopus 로고
    • Interface Dynamics
    • (in Japanese)
    • [Ohta 1997] T. Ohta, Interface Dynamics, Nippon Hyoronsha (1997) (in Japanese).
    • (1997) Nippon Hyoronsha
    • Ohta, T.1
  • 203
    • 0342551040 scopus 로고    scopus 로고
    • Exact solutions of the Navier-Stokes equations via Leray’s scheme
    • [Okamoto 1997] H. Okamoto, Exact solutions of the Navier-Stokes equations via Leray’s scheme, Japan J. Indust. Appl. Math., 14 (1997), 169–197.
    • (1997) Japan J. Indust. Appl. Math. , vol.14 , pp. 169-197
    • Okamoto, H.1
  • 204
    • 0040102518 scopus 로고
    • Diffusion processes with generators of generalized divergence form
    • [Osada 1987] H. Osada, Diffusion processes with generators of generalized divergence form, J. Math. Kyoto Univ. 27 (1987), 597–619.
    • (1987) J. Math. Kyoto Univ. , vol.27 , pp. 597-619
    • Osada, H.1
  • 205
    • 0000506513 scopus 로고
    • On critical cases of Sobolev’s inequalities
    • [Ozawa 1995] T. Ozawa, On critical cases of Sobolev’s inequalities, J. Funct. Anal., 127 (1995), 259–269.
    • (1995) J. Funct. Anal. , vol.127 , pp. 259-269
    • Ozawa, T.1
  • 207
    • 0039468127 scopus 로고    scopus 로고
    • Scattering theory of nonlinear Schrödinger equations
    • (in Japanese)
    • [Ozawa 1998] T. Ozawa, Scattering theory of nonlinear Schrödinger equations, Sûgaku, 50 (1998), 337–349 (in Japanese).
    • (1998) Sûgaku , vol.50 , pp. 337-349
    • Ozawa, T.1
  • 209
    • 34249807607 scopus 로고    scopus 로고
    • Singularity and decay estimates in superlinear problems via Liouville-type theorems, Part II: Parabolic equations
    • [Polacik Quittner Souplet 2007] P. Poláčik, P. Quittner, and P. Souplet, Singularity and decay estimates in superlinear problems via Liouville-type theorems, Part II: Parabolic equations, Indiana Univ. Math. J., 56 (2007), 879–908.
    • (2007) Indiana Univ. Math. J. , vol.56 , pp. 879-908
    • Poláčik, P.1    Quittner, P.2    Souplet, P.3
  • 210
    • 0032071912 scopus 로고    scopus 로고
    • Structure and stability of non-symmetric Burgers vortices
    • [Prochazka Pullin 1998] A. Prochazka and D. I. Pullin, Structure and stability of non-symmetric Burgers vortices, J. Fluid Mech., 363 (1998), 199–228.
    • (1998) J. Fluid Mech. , vol.363 , pp. 199-228
    • Prochazka, A.1    Pullin, D.I.2
  • 211
    • 85045459279 scopus 로고
    • Maximum principles in differential equations, Englewood Cliffs
    • [Protter Weinberger 1967] Maximum principles in differential equations, Englewood Cliffs, N. J. Printice-Hall, (1967).
    • (1967) N. J. Printice-Hall
  • 212
    • 36849054783 scopus 로고    scopus 로고
    • Blow-up, global existence and steady states, Birkhäuser Advanced Texts, Birkhäuser
    • [Quittner Souplet 2007] P. Quittner and P. Souplet, Superlinear parabolic problems. Blow-up, global existence and steady states, Birkhäuser Advanced Texts, Birkhäuser (2007).
    • (2007) Superlinear Parabolic Problems
    • Quittner, P.1    Souplet, P.2
  • 215
    • 0032324914 scopus 로고    scopus 로고
    • Regular and self-similar solutions of nonlinear Schrödinger equations
    • [Ribaud Youssfi 1998] F. Ribaud and A. Youssfi, Regular and self-similar solutions of nonlinear Schrödinger equations, J. Math. Pures Appl., 77 (1998), 1065–1079
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 1065-1079
    • Ribaud, F.1    Youssfi, A.2
  • 216
    • 0021416031 scopus 로고
    • Stability and structure of stretched vortices
    • [Robinson Saffman 1984] A. C. Robinson and P. G. Saffman, Stability and structure of stretched vortices, Stud. Appl. Math., 70(2) (1984), 163–181.
    • (1984) Stud. Appl. Math. , vol.70 , Issue.2 , pp. 163-181
    • Robinson, A.C.1    Saffman, P.G.2
  • 218
    • 0004116414 scopus 로고
    • third edition, McGraw-Hill, New York
    • [Rudin 1987] W. Rudin, Real and complex analysis, third edition, McGraw-Hill, New York (1987).
    • (1987) Real and Complex Analysis
    • Rudin, W.1
  • 219
    • 33748541987 scopus 로고    scopus 로고
    • Stokes and Navier-Stokes equations with Robin boundary conditions in a half-space
    • [Saal 2006] J. Saal, Stokes and Navier-Stokes equations with Robin boundary conditions in a half-space, J. Math. Fluid Mech., 8 (2006), 211–241.
    • (2006) J. Math. Fluid Mech. , vol.8 , pp. 211-241
    • Saal, J.1
  • 220
    • 84867550339 scopus 로고    scopus 로고
    • Strong solutions for the Navier-Stokes equations on bounded and unbounded domains with a moving boundary
    • [Saal 2007a] J. Saal, Strong solutions for the Navier-Stokes equations on bounded and unbounded domains with a moving boundary, Electron. J. Differential Equations and Conf., 15 (2007), 365–375.
    • (2007) Electron. J. Differential Equations and Conf. , vol.15 , pp. 365-375
    • Saal, J.1
  • 221
    • 84960495669 scopus 로고    scopus 로고
    • Existence and regularity of weak solutions for the Navier-Stokes equations with partial slip boundary conditions
    • [Saal 2007b] J. Saal, Existence and regularity of weak solutions for the Navier-Stokes equations with partial slip boundary conditions, RIMS Kokyuroku Bessatsu, B1 (2007), 331–342.
    • (2007) RIMS Kokyuroku Bessatsu , vol.B1 , pp. 331-342
    • Saal, J.1
  • 222
    • 30844468837 scopus 로고    scopus 로고
    • Regularity theorems for parabolic equations
    • [Samenov 2006] Y. A. Samenov, Regularity theorems for parabolic equations, J. Funct. Anal., 231 (2006), 375–417.
    • (2006) J. Funct. Anal. , vol.231 , pp. 375-417
    • Samenov, Y.A.1
  • 223
    • 1542287311 scopus 로고    scopus 로고
    • Three-dimensional stability of a Burgers vortex
    • [Schmid Rossi 2004] P. J. Schmid and M. Rossi, Three-dimensional stability of a Burgers vortex, J. Fluid Mech., 500 (2004), 103–112.
    • (2004) J. Fluid Mech. , vol.500 , pp. 103-112
    • Schmid, P.J.1    Rossi, M.2
  • 225
    • 0004096780 scopus 로고
    • Lectures on geometric measure theory, Proc. Of the Centre of Mathematical Analysis
    • [Simon 1983] L. Simon, Lectures on geometric measure theory, Proc. of the Centre of Mathematical Analysis, Australian National University, 3 (1983).
    • (1983) Australian National University , pp. 3
    • Simon, L.1
  • 227
    • 0001283493 scopus 로고
    • Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature
    • [Soner Souganidis 1993] H. M. Soner and P. E. Souganidis, Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature, Commun. in Partial Differential Equations, 18 (1993), 859–894.
    • (1993) Commun. in Partial Differential Equations , vol.18 , pp. 859-894
    • Soner, H.M.1    Souganidis, P.E.2
  • 228
    • 22844454513 scopus 로고    scopus 로고
    • Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term
    • [Snoussi Tayachi Weissler 1999] S. Snoussi, S. Tayachi, and F. B. Weissler, Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term, Proc. Roy. Soc. Edinburgh Sect. A, 129 (1999), 1291–1307.
    • (1999) Proc. Roy. Soc. Edinburgh Sect. A , vol.129 , pp. 1291-1307
    • Snoussi, S.1    Tayachi, S.2    Weissler, F.B.3
  • 229
    • 0035601963 scopus 로고    scopus 로고
    • Asymptotically self-similar global solutions of a general semilinear heat equation
    • [Snoussi Tayachi Weissler 2001] S. Snoussi, S. Tayachi, and F. B. Weissler, Asymptotically self-similar global solutions of a general semilinear heat equation, Math. Ann., 321 (2001), 131–155.
    • (2001) Math. Ann. , vol.321 , pp. 131-155
    • Snoussi, S.1    Tayachi, S.2    Weissler, F.B.3
  • 230
    • 0033474488 scopus 로고    scopus 로고
    • Geometry of unbounded domains, Poincaré inequalities and stability in semilinear heat equations
    • [Souplet 1999] P. Souplet, Geometry of unbounded domains, Poincaré inequalities and stability in semilinear heat equations, Comm. Partial Differential Equations, 24 (1999), 951–973.
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 951-973
    • Souplet, P.1
  • 231
    • 0347354923 scopus 로고    scopus 로고
    • Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state
    • [Souplet Weissler 2003] P. Souplet and F. B. Weissler, Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), 213–235.
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , pp. 213-235
    • Souplet, P.1    Weissler, F.B.2
  • 233
    • 0003552286 scopus 로고
    • Princeton University Press
    • [Stein 1993] E. M. Stein, Harmonic analysis, Princeton University Press (1993).
    • (1993) Harmonic Analysis
    • Stein, E.M.1
  • 235
    • 84972503995 scopus 로고
    • On the evolution of harmonic maps in higher dimensions
    • [Struwe 1988] M. Struwe, On the evolution of harmonic maps in higher dimensions, J. Differential Geometry, 28 (1988), 485–502.
    • (1988) J. Differential Geometry , vol.28 , pp. 485-502
    • Struwe, M.1
  • 236
    • 0002341651 scopus 로고    scopus 로고
    • Geometric evolution problems, “Nonlinear partial differential equations in differential geometry”
    • R. Hardt, M. Wolf, eds
    • [Struwe 1996] M. Struwe, Geometric evolution problems, “Nonlinear partial differential equations in differential geometry”, (R. Hardt, M. Wolf, eds.) Amer. Math. Soc. (1996), 257–339.
    • (1996) Amer. Math. Soc. , pp. 257-339
    • Struwe, M.1
  • 237
    • 0004062360 scopus 로고
    • Translated from the 1975 Japanese original published by Iwanami, Tokyo
    • [Tanabe 1975] H. Tanabe, Equations of evolution, Pitman, Boston (1979). Translated from the 1975 Japanese original published by Iwanami, Tokyo.
    • (1979) Equations of Evolution, Pitman, Boston
    • Tanabe, H.1
  • 238
    • 0003430382 scopus 로고    scopus 로고
    • Marcel Dekker Inc. New York (1997). (Expanded from the Japanese edition “Functional Analysis” published by Jikkyo Shuppan (two volumes), Tokyo (1981))
    • [Tanabe 1981] H. Tanabe, Functional Analytic Methods for Partial Differential Equations, Marcel Dekker Inc. New York (1997). (Expanded from the Japanese edition “Functional Analysis” published by Jikkyo Shuppan (two volumes), Tokyo (1981)).
    • Functional Analytic Methods for Partial Differential Equations
    • Tanabe, H.1
  • 239
    • 0000830871 scopus 로고
    • Analysis on Morrey spaces and applications to the Navier-Stokes and other evolution equations
    • [Taylor 1992] M. E. Taylor, Analysis on Morrey spaces and applications to the Navier-Stokes and other evolution equations, Comm. Partial Differential Equations, 17 (1992), 1407–1456.
    • (1992) Comm. Partial Differential Equations , vol.17 , pp. 1407-1456
    • Taylor, M.E.1
  • 242
    • 4644221893 scopus 로고    scopus 로고
    • Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow
    • [Topping 2004] P. Topping, Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow, Ann. of Math., (2) 159 (2004), 465–534.
    • (2004) Ann. of Math. , vol.159 , Issue.2 , pp. 465-534
    • Topping, P.1
  • 248
    • 0013061261 scopus 로고
    • The existence of bounded solutions of a semilinear heat equations
    • [Troy 1987] W. Troy, The existence of bounded solutions of a semilinear heat equations, SIAM J. Math. Anal., 18 (1987), 332–336.
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 332-336
    • Troy, W.1
  • 249
    • 0000453612 scopus 로고
    • On imbeddings into Orlicz spaces and some applications
    • [Trudinger 1967] N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech., 17 (1967), 473–483.
    • (1967) J. Math. Mech. , vol.17 , pp. 473-483
    • Trudinger, N.S.1
  • 250
    • 0032363760 scopus 로고    scopus 로고
    • On Leray’s self-similar solutions of the Navier-Stokes equations satisfying local energy estimates
    • Erratum, ibid. 147 (1999), 363
    • [Tsai 1998] T. P. Tsai, On Leray’s self-similar solutions of the Navier-Stokes equations satisfying local energy estimates, Arch. Rational Mech. Anal., 143 (1998), 29–51; Erratum, ibid. 147 (1999), 363.
    • (1998) Arch. Rational Mech. Anal. , vol.143 , pp. 29-51
    • Tsai, T.P.1
  • 251
    • 85045468462 scopus 로고    scopus 로고
    • Translated from the Japanese original in Sûgaku, 47 (1995), 18–37
    • [Tsutsumi 1995] M. Tsutsumi, The nonlinear Schrödinger equation, Sugaku Exposition, 10 (1997), 159–182. Translated from the Japanese original in Sûgaku, 47 (1995), 18–37.
    • (1997) The Nonlinear Schrödinger Equation, Sugaku Exposition , vol.10 , pp. 159-182
    • Tsutsumi, M.1
  • 252
    • 0003226423 scopus 로고
    • Calculus of Variations and Harmonic Maps
    • Translated from the 1990 Japanese original published by Shokabo, Tokyo
    • [Urakawa 1990] H. Urakawa, Calculus of Variations and Harmonic Maps, Amer. Math. Soc (1993). Translated from the 1990 Japanese original published by Shokabo, Tokyo.
    • (1993) Amer. Math. Soc
    • Urakawa, H.1
  • 255
    • 84894531156 scopus 로고    scopus 로고
    • Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford
    • [Vázquez 2007] J. L. Vázquez, The porous medium equation, Mathematical theory. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford (2007).
    • (2007) The Porous Medium Equation, Mathematical Theory
    • Vázquez, J.L.1
  • 256
    • 0035629005 scopus 로고    scopus 로고
    • p-regularity
    • p-regularity, Math. Ann., 319 (4) (2001), 29–40.
    • (2001) Math. Ann. , vol.319 , Issue.4 , pp. 29-40
    • Weis, L.1
  • 257
    • 51249183619 scopus 로고
    • Existence and non-existence of global solutions for a semilinear heat equation
    • [Weissler 1981] F. B. Weissler, Existence and non-existence of global solutions for a semilinear heat equation, Israel J. Math., 38 (1981), 29–40.
    • (1981) Israel J. Math. , vol.38 , pp. 29-40
    • Weissler, F.B.1
  • 258
    • 0000357569 scopus 로고
    • Asymptotic analysis of an ordinary differential equation and nonuniqueness for a semilinear partial differential equation
    • [Weissler 1985a] F. B. Weissler, Asymptotic analysis of an ordinary differential equation and nonuniqueness for a semilinear partial differential equation, Arch. Rational Mech. Anal., 91 (1985), 231–245.
    • (1985) Arch. Rational Mech. Anal. , vol.91 , pp. 231-245
    • Weissler, F.B.1
  • 259
    • 0001631515 scopus 로고
    • Rapidly decaying solutions of an ordinary differential equation with applications to semilinear elliptic and parabolic partial differential equations
    • [Weissler 1985b] F. B. Weissler, Rapidly decaying solutions of an ordinary differential equation with applications to semilinear elliptic and parabolic partial differential equations, Arch. Rational Mech. Anal., 91 (1985), 247–266.
    • (1985) Arch. Rational Mech. Anal. , vol.91 , pp. 247-266
    • Weissler, F.B.1
  • 260
  • 261
    • 67649603876 scopus 로고    scopus 로고
    • Navier-Stokes equations in various functions spaces
    • (in Japanese)
    • [Yamazaki 1999] M. Yamazaki, Navier-Stokes equations in various functions spaces, Sûgaku 51 (1999), 291–308 (in Japanese).
    • (1999) Sûgaku , vol.51 , pp. 291-308
    • Yamazaki, M.1
  • 262
    • 0030594472 scopus 로고    scopus 로고
    • Uniqueness of rapidly decaying solutions to the Haraux-Weissler equation
    • [Yanagida 1996] E. Yanagida, Uniqueness of rapidly decaying solutions to the Haraux-Weissler equation. J. Differential Equations 127 (1996), 561–570.
    • (1996) J. Differential Equations , vol.127 , pp. 561-570
    • Yanagida, E.1
  • 264
    • 85045434619 scopus 로고
    • Iwanami, Tokyo, (in Japanese)
    • [Yosida 1976] K. Yosida, Measures and integrals, Iwanami, Tokyo (1976) (in Japanese).
    • (1976) Measures and Integrals
    • Yosida, K.1
  • 266
    • 0038441036 scopus 로고
    • Fractional powers of operators, interpolation theory and embedding theorems
    • [Yoshikawa 1971] A. Yoshikawa, Fractional powers of operators, interpolation theory and embedding theorems, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 18 (1971), 335–362.
    • (1971) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.18 , pp. 335-362
    • Yoshikawa, A.1
  • 267
    • 0001883857 scopus 로고
    • Stabilization of solutions of boundary value problem for a second-order parabolic equations with one space variable
    • [Zelenyak 1968] T. I. Zelenyak, Stabilization of solutions of boundary value problem for a second-order parabolic equations with one space variable, Differential Equations (trans. of Diff. Uravneniya), 4 (1968), 17–22.
    • (1968) Differential Equations (Trans. of Diff. Uravneniya) , vol.4 , pp. 17-22
    • Zelenyak, T.I.1
  • 268
    • 0842325112 scopus 로고    scopus 로고
    • A strong regularity result for parabolic equations
    • [Zhang 2004] Q. S. Zhang, A strong regularity result for parabolic equations, Comm. Math. Phys., 224 no. 2 (2004), 245–260.
    • (2004) Comm. Math. Phys. , vol.224 , Issue.2 , pp. 245-260
    • Zhang, Q.S.1
  • 269
    • 32344452439 scopus 로고    scopus 로고
    • Local estimates on two linear parabolic equations with singular coefficients
    • [Zhang 2006] Q. S. Zhang, Local estimates on two linear parabolic equations with singular coefficients, Pacific J. Math., 223 no. 3 (2006), 367–396.
    • (2006) Pacific J. Math. , vol.223 , Issue.3 , pp. 367-396
    • Zhang, Q.S.1


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