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Volumn 202, Issue 1, 2011, Pages 35-62

Inviscid Models Generalizing the Two-dimensional Euler and the Surface Quasi-geostrophic Equations

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EID: 80052418503     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-011-0411-5     Document Type: Article
Times cited : (130)

References (102)
  • 1
    • 61849151015 scopus 로고    scopus 로고
    • On the global well-posedness of the critical quasi-geostrophic equation
    • Abidi H., Hmidi T.: On the global well-posedness of the critical quasi-geostrophic equation. SIAM J. Math. Anal. 40, 167-185 (2008).
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 167-185
    • Abidi, H.1    Hmidi, T.2
  • 2
    • 77950613331 scopus 로고    scopus 로고
    • Global well-posedness of dissipative quasi-geostrophic equations in critical spaces
    • Bae H.: Global well-posedness of dissipative quasi-geostrophic equations in critical spaces. Proc. Am. Math. Soc. 136, 257-261 (2008).
    • (2008) Proc. Am. Math. Soc. , vol.136 , pp. 257-261
    • Bae, H.1
  • 5
    • 0010414321 scopus 로고
    • Uniform potential vorticity flow, Part I. Theory of wave interactions and two-dimensional turbulence
    • Blumen W.: Uniform potential vorticity flow, Part I. Theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci. 35, 774-783 (1978).
    • (1978) J. Atmos. Sci. , vol.35 , pp. 774-783
    • Blumen, W.1
  • 6
    • 34548348805 scopus 로고    scopus 로고
    • An extension problem related to the fractional Laplacian
    • Caffarelli L., Silvestre L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 32, 1245-1260 (2007).
    • (2007) Commun. Partial Differ. Equ. , vol.32 , pp. 1245-1260
    • Caffarelli, L.1    Silvestre, L.2
  • 7
    • 77950869887 scopus 로고    scopus 로고
    • Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
    • Caffarelli L., Vasseur A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. Math. 171, 1903-1930 (2010).
    • (2010) Ann. Math. , vol.171 , pp. 1903-1930
    • Caffarelli, L.1    Vasseur, A.2
  • 8
    • 43049083362 scopus 로고    scopus 로고
    • The asymptotic behaviour of subcritical dissipative quasi-geostrophic equations
    • Carrillo J., Ferreira L.: The asymptotic behaviour of subcritical dissipative quasi-geostrophic equations. Nonlinearity 21, 1001-1018 (2008).
    • (2008) Nonlinearity , vol.21 , pp. 1001-1018
    • Carrillo, J.1    Ferreira, L.2
  • 9
    • 0242276370 scopus 로고    scopus 로고
    • The quasi-geostrophic equation in the Triebel-Lizorkin spaces
    • Chae D.: The quasi-geostrophic equation in the Triebel-Lizorkin spaces. Nonlinearity 16, 479-495 (2003).
    • (2003) Nonlinearity , vol.16 , pp. 479-495
    • Chae, D.1
  • 10
    • 33646703120 scopus 로고    scopus 로고
    • On the continuation principles for the Euler equations and the quasi-geostrophic equation
    • Chae D.: On the continuation principles for the Euler equations and the quasi-geostrophic equation. J. Differ. Equ. 227, 640-651 (2006).
    • (2006) J. Differ. Equ. , vol.227 , pp. 640-651
    • Chae, D.1
  • 11
    • 33748882638 scopus 로고    scopus 로고
    • On the regularity conditions for the dissipative quasi-geostrophic equations
    • Chae D.: On the regularity conditions for the dissipative quasi-geostrophic equations. SIAM J. Math. Anal. 37, 1649-1656 (2006).
    • (2006) SIAM J. Math. Anal. , vol.37 , pp. 1649-1656
    • Chae, D.1
  • 12
    • 54749092935 scopus 로고    scopus 로고
    • The geometric approaches to the possible singularities in the inviscid fluid flows
    • Chae D.: The geometric approaches to the possible singularities in the inviscid fluid flows. J. Phys. A 41, 365501-365511 (2008).
    • (2008) J. Phys. A , vol.41 , pp. 365501-365511
    • Chae, D.1
  • 13
    • 67349244092 scopus 로고    scopus 로고
    • On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations
    • Chae D.: On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations. Adv. Math. 221, 1678-1702 (2009).
    • (2009) Adv. Math. , vol.221 , pp. 1678-1702
    • Chae, D.1
  • 14
    • 16244382542 scopus 로고    scopus 로고
    • Finite time singularities in a 1D model of the quasi-geostrophic equation
    • Chae D., Córdoba A., Córdoba D., Fontelos M.: Finite time singularities in a 1D model of the quasi-geostrophic equation. Adv. Math. 194, 203-223 (2005).
    • (2005) Adv. Math. , vol.194 , pp. 203-223
    • Chae, D.1    Córdoba, A.2    Córdoba, D.3    Fontelos, M.4
  • 15
    • 0037330176 scopus 로고    scopus 로고
    • Global well-posedness in the super-critical dissipative quasi-geostrophic equations
    • Chae D., Lee J.: Global well-posedness in the super-critical dissipative quasi-geostrophic equations. Commun. Math. Phys. 233, 297-311 (2003).
    • (2003) Commun. Math. Phys. , vol.233 , pp. 297-311
    • Chae, D.1    Lee, J.2
  • 16
    • 80052397420 scopus 로고
    • Astérisque, Société Mathématique de France
    • Chemin J.-Y.: Fluides parfaits incompressibles, Astérisque No. 230. Société Mathématique de France, 1995.
    • (1995) Fluides parfaits incompressibles , vol.230
    • Chemin, J.-Y.1
  • 17
    • 33947403194 scopus 로고    scopus 로고
    • A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
    • Chen Q., Miao C., Zhang Z.: A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation. Commun. Math. Phys. 271, 821-838 (2007).
    • (2007) Commun. Math. Phys. , vol.271 , pp. 821-838
    • Chen, Q.1    Miao, C.2    Zhang, Z.3
  • 18
    • 34247366059 scopus 로고    scopus 로고
    • Global well-posedness of the 2D critical dissipative quasi-geostrophic equation in the Triebel-Lizorkin spaces
    • Chen Q., Zhang Z.: Global well-posedness of the 2D critical dissipative quasi-geostrophic equation in the Triebel-Lizorkin spaces. Nonlinear Anal. 67, 1715-1725 (2007).
    • (2007) Nonlinear Anal. , vol.67 , pp. 1715-1725
    • Chen, Q.1    Zhang, Z.2
  • 19
    • 33748858288 scopus 로고    scopus 로고
    • Euler equations, Navier-Stokes equations and turbulence
    • Lecture Notes in Mathematics, Springer, Berlin
    • Constantin P.: Euler equations, Navier-Stokes equations and turbulence. Mathematical foundation of turbulent viscous flows. Lecture Notes in Mathematics, Vol. 1871. Springer, Berlin, 1-43, 2006.
    • (2006) Mathematical foundation of turbulent viscous flows , vol.1871 , pp. 1-43
    • Constantin, P.1
  • 20
    • 0002223508 scopus 로고    scopus 로고
    • On the critical dissipative quasi-geostrophic equation
    • Constantin P., Córdoba D., Wu J.: On the critical dissipative quasi-geostrophic equation. Indiana Univ. Math. J. 50, 97-107 (2001).
    • (2001) Indiana Univ. Math. J. , vol.50 , pp. 97-107
    • Constantin, P.1    Córdoba, D.2    Wu, J.3
  • 21
    • 59549099483 scopus 로고    scopus 로고
    • Global regularity for a modified critical dissipative quasi-geostrophic equation
    • Constantin P., Iyer G., Wu J.: Global regularity for a modified critical dissipative quasi-geostrophic equation. Indiana Univ. Math. J. 57, 2681-2692 (2008).
    • (2008) Indiana Univ. Math. J. , vol.57 , pp. 2681-2692
    • Constantin, P.1    Iyer, G.2    Wu, J.3
  • 23
    • 0043172071 scopus 로고
    • Formation of strong fronts in the 2-D quasi-geostrophic thermal active scalar
    • Constantin P., Majda A., Tabak E.: Formation of strong fronts in the 2-D quasi-geostrophic thermal active scalar. Nonlinearity 7, 1495-1533 (1994).
    • (1994) Nonlinearity , vol.7 , pp. 1495-1533
    • Constantin, P.1    Majda, A.2    Tabak, E.3
  • 24
    • 0000579087 scopus 로고    scopus 로고
    • Nonsingular surface quasi-geostrophic flow
    • Constantin P., Nie Q., Schorghofer N.: Nonsingular surface quasi-geostrophic flow. Phys. Lett. A 241, 168-172 (1998).
    • (1998) Phys. Lett. A , vol.241 , pp. 168-172
    • Constantin, P.1    Nie, Q.2    Schorghofer, N.3
  • 25
    • 0033419179 scopus 로고    scopus 로고
    • Behavior of solutions of 2D quasi-geostrophic equations
    • Constantin P., Wu J.: Behavior of solutions of 2D quasi-geostrophic equations. SIAM J. Math. Anal. 30, 937-948 (1999).
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 937-948
    • Constantin, P.1    Wu, J.2
  • 26
    • 54549116855 scopus 로고    scopus 로고
    • Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
    • Constantin P., Wu J.: Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 25, 1103-1110 (2008).
    • (2008) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.25 , pp. 1103-1110
    • Constantin, P.1    Wu, J.2
  • 27
    • 58249085827 scopus 로고    scopus 로고
    • Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equation
    • Constantin P., Wu J.: Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 26, 159-180 (2009).
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , pp. 159-180
    • Constantin, P.1    Wu, J.2
  • 28
    • 0032264533 scopus 로고    scopus 로고
    • Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation
    • Córdoba D.: Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation. Ann. Math. 148, 1135-1152 (1998).
    • (1998) Ann. Math. , vol.148 , pp. 1135-1152
    • Córdoba, D.1
  • 29
    • 4544377751 scopus 로고    scopus 로고
    • A maximum principle applied to quasi-geostrophic equations
    • Córdoba A., Córdoba D.: A maximum principle applied to quasi-geostrophic equations. Commun. Math. Phys. 249, 511-528 (2004).
    • (2004) Commun. Math. Phys. , vol.249 , pp. 511-528
    • Córdoba, A.1    Córdoba, D.2
  • 30
    • 0035836678 scopus 로고    scopus 로고
    • Behavior of several two-dimensional fluid equations in singular scenarios
    • Córdoba D., Fefferman Ch.: Behavior of several two-dimensional fluid equations in singular scenarios. Proc. Natl. Acad. Sci. USA 98, 4311-4312 (2001).
    • (2001) Proc. Natl. Acad. Sci. USA , vol.98 , pp. 4311-4312
    • Córdoba, D.1    Fefferman, C.2
  • 31
    • 0036220103 scopus 로고    scopus 로고
    • Scalars convected by a two-dimensional incompressible flow
    • Córdoba D., Fefferman Ch.: Scalars convected by a two-dimensional incompressible flow. Commun. Pure Appl. Math. 55, 255-260 (2002).
    • (2002) Commun. Pure Appl. Math. , vol.55 , pp. 255-260
    • Córdoba, D.1    Fefferman, C.2
  • 32
    • 0036016138 scopus 로고    scopus 로고
    • Growth of solutions for QG and 2D Euler equations
    • Córdoba D., Fefferman Ch.: Growth of solutions for QG and 2D Euler equations. J. Am. Math. Soc. 15, 665-670 (2002).
    • (2002) J. Am. Math. Soc. , vol.15 , pp. 665-670
    • Córdoba, D.1    Fefferman, C.2
  • 33
    • 17844380780 scopus 로고    scopus 로고
    • Evidence of singularities for a family of contour dynamics equations
    • Córdoba D., Fontelos M., Mancho A., Rodrigo J.: Evidence of singularities for a family of contour dynamics equations. Proc. Natl. Acad. Sci. USA 102, 5949-5952 (2005).
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 5949-5952
    • Córdoba, D.1    Fontelos, M.2    Mancho, A.3    Rodrigo, J.4
  • 35
    • 70350569716 scopus 로고    scopus 로고
    • Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation
    • Deng J., Hou T. Y., Li R., Yu X.: Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Methods Appl. Anal. 13, 157-180 (2006).
    • (2006) Methods Appl. Anal. , vol.13 , pp. 157-180
    • Deng, J.1    Hou, T.Y.2    Li, R.3    Yu, X.4
  • 36
    • 33846117131 scopus 로고    scopus 로고
    • Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation
    • Dong B., Chen Z.: Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation. Nonlinearity 19, 2919-2928 (2006).
    • (2006) Nonlinearity , vol.19 , pp. 2919-2928
    • Dong, B.1    Chen, Z.2
  • 37
    • 77950223071 scopus 로고    scopus 로고
    • Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness
    • Dong H.: Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness. Discrete Contin. Dyn. Syst. 26, 1197-1211 (2010).
    • (2010) Discrete Contin. Dyn. Syst. , vol.26 , pp. 1197-1211
    • Dong, H.1
  • 38
    • 50249090960 scopus 로고    scopus 로고
    • Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
    • Dong H., Du D.: Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Discrete Contin. Dyn. Syst. 21, 1095-1101 (2008).
    • (2008) Discrete Contin. Dyn. Syst. , vol.21 , pp. 1095-1101
    • Dong, H.1    Du, D.2
  • 39
    • 54949154201 scopus 로고    scopus 로고
    • Finite time singularities for a class of generalized surface quasi-geostrophic equations
    • Dong H., Li D.: Finite time singularities for a class of generalized surface quasi-geostrophic equations. Proc. Am. Math. Soc. 136, 2555-2563 (2008).
    • (2008) Proc. Am. Math. Soc. , vol.136 , pp. 2555-2563
    • Dong, H.1    Li, D.2
  • 40
    • 43749097438 scopus 로고    scopus 로고
    • Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations
    • Dong H., Li D.: Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Arch. Ration. Mech. Anal. 189, 131-158 (2008).
    • (2008) Arch. Ration. Mech. Anal. , vol.189 , pp. 131-158
    • Dong, H.1    Li, D.2
  • 41
    • 69749083481 scopus 로고    scopus 로고
    • A regularity criterion for the dissipation quasi-geostrophic equation
    • Dong H., Pavlovic N.: A regularity criterion for the dissipation quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 26, 1607-1619 (2009).
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , pp. 1607-1619
    • Dong, H.1    Pavlovic, N.2
  • 42
    • 70349918312 scopus 로고    scopus 로고
    • Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces
    • Dong H., Pavlovic N.: Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces. Commun. Math. Phys. 290, 801-812 (2009).
    • (2009) Commun. Math. Phys. , vol.290 , pp. 801-812
    • Dong, H.1    Pavlovic, N.2
  • 43
    • 70350580506 scopus 로고    scopus 로고
    • Nonlinear instability for the critically dissipative quasi-geostrophic equation
    • Friedlander S., Pavlovic N., Vicol V.: Nonlinear instability for the critically dissipative quasi-geostrophic equation. Commun. Math. Phys. 292, 797-810 (2009).
    • (2009) Commun. Math. Phys. , vol.292 , pp. 797-810
    • Friedlander, S.1    Pavlovic, N.2    Vicol, V.3
  • 47
    • 34447123394 scopus 로고    scopus 로고
    • Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces
    • Hmidi T., Keraani S.: Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces. Adv. Math. 214, 618-638 (2007).
    • (2007) Adv. Math. , vol.214 , pp. 618-638
    • Hmidi, T.1    Keraani, S.2
  • 48
    • 61849151015 scopus 로고    scopus 로고
    • On the global well-posedness of the critical quasi-geostrophic equation
    • Hmidi T., Keraani S.: On the global well-posedness of the critical quasi-geostrophic equation. SIAM J. Math. Anal. 40, 167-185 (2008).
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 167-185
    • Hmidi, T.1    Keraani, S.2
  • 49
    • 21244497902 scopus 로고    scopus 로고
    • The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations
    • Ju N.: The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations. Commun. Math. Phys. 255, 161-181 (2005).
    • (2005) Commun. Math. Phys. , vol.255 , pp. 161-181
    • Ju, N.1
  • 50
    • 33646589946 scopus 로고    scopus 로고
    • Geometric constrains for global regularity of 2D quasi-geostrophic flows
    • Ju N.: Geometric constrains for global regularity of 2D quasi-geostrophic flows. J. Differ. Equ. 226, 54-79 (2006).
    • (2006) J. Differ. Equ. , vol.226 , pp. 54-79
    • Ju, N.1
  • 51
    • 52349110039 scopus 로고    scopus 로고
    • An inviscid regularization for the surface quasi-geostrophic equation
    • Khouider B., Titi E.: An inviscid regularization for the surface quasi-geostrophic equation. Commun. Pure Appl. Math. 61, 1331-1346 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , pp. 1331-1346
    • Khouider, B.1    Titi, E.2
  • 52
    • 80052421465 scopus 로고    scopus 로고
    • Some recent results on the critical surface quasi-geostrophic equation: a review. Hyperbolic problems: theory, numerics and applications
    • AMS, Providence, RI
    • Kiselev A.: Some recent results on the critical surface quasi-geostrophic equation: a review. Hyperbolic problems: theory, numerics and applications. Proc. Sympos. Appl. Math., Vol. 67, Part 1. AMS, Providence, RI, 105-122, 2009.
    • (2009) Proc. Sympos. Appl. Math. , vol.67 , Issue.PART 1 , pp. 105-122
    • Kiselev, A.1
  • 53
    • 79959227806 scopus 로고    scopus 로고
    • Regularity and blow up for active scalars
    • Kiselev A.: Regularity and blow up for active scalars. Math. Model. Math. Phenom. 5, 225-255 (2010).
    • (2010) Math. Model. Math. Phenom. , vol.5 , pp. 225-255
    • Kiselev, A.1
  • 54
    • 75149114116 scopus 로고    scopus 로고
    • Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation
    • Kiselev A., Nazarov F.: Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation. Nonlinearity 23, 549-554 (2010).
    • (2010) Nonlinearity , vol.23 , pp. 549-554
    • Kiselev, A.1    Nazarov, F.2
  • 55
    • 79956352191 scopus 로고    scopus 로고
    • A variation on a theme of Caffarelli and Vasseur
    • Kiselev A., Nazarov F.: A variation on a theme of Caffarelli and Vasseur. Zap. Nauchn. Sem. POMI 370, 58-72 (2010).
    • (2010) Zap. Nauchn. Sem. POMI , vol.370 , pp. 58-72
    • Kiselev, A.1    Nazarov, F.2
  • 56
    • 33846785446 scopus 로고    scopus 로고
    • Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
    • Kiselev A., Nazarov F., Volberg A.: Global well-posedness for the critical 2D dissipative quasi-geostrophic equation. Invent. Math. 167, 445-453 (2007).
    • (2007) Invent. Math. , vol.167 , pp. 445-453
    • Kiselev, A.1    Nazarov, F.2    Volberg, A.3
  • 58
    • 67650757418 scopus 로고    scopus 로고
    • Existence theorems for the 2D quasi-geostrophic equation with plane wave initial conditions
    • Li D.: Existence theorems for the 2D quasi-geostrophic equation with plane wave initial conditions. Nonlinearity 22, 1639-1651 (2009).
    • (2009) Nonlinearity , vol.22 , pp. 1639-1651
    • Li, D.1
  • 59
    • 58149492604 scopus 로고    scopus 로고
    • Blow up for the generalized surface quasi-geostrophic equation with supercritical dissipation
    • Li D., Rodrigo J.: Blow up for the generalized surface quasi-geostrophic equation with supercritical dissipation. Commun. Math. Phys. 286, 111-124 (2009).
    • (2009) Commun. Math. Phys. , vol.286 , pp. 111-124
    • Li, D.1    Rodrigo, J.2
  • 60
    • 0141689565 scopus 로고    scopus 로고
    • Courant Lecture Notes, Courant Institute of Mathematical Sciences and American Mathematical Society
    • Majda A.: Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes, Vol. 9. Courant Institute of Mathematical Sciences and American Mathematical Society, 2003.
    • (2003) Introduction to PDEs and Waves for the Atmosphere and Ocean , vol.9
    • Majda, A.1
  • 62
    • 0000669501 scopus 로고    scopus 로고
    • A two-dimensional model for quasigeostrophic flow: comparison with the two-dimensional Euler flow
    • Majda A., Tabak E.: A two-dimensional model for quasigeostrophic flow: comparison with the two-dimensional Euler flow. Phys. D 98, 515-522 (1996).
    • (1996) Phys. D , vol.98 , pp. 515-522
    • Majda, A.1    Tabak, E.2
  • 63
    • 33748924502 scopus 로고    scopus 로고
    • Propagation of Sobolev regularity for the critical dissipative quasi-geostrophic equation
    • Marchand F.: Propagation of Sobolev regularity for the critical dissipative quasi-geostrophic equation. Asymptot. Anal. 49, 275-293 (2006).
    • (2006) Asymptot. Anal. , vol.49 , pp. 275-293
    • Marchand, F.1
  • 65
    • 44649105674 scopus 로고    scopus 로고
    • Weak-strong uniqueness criteria for the critical quasi-geostrophic equation
    • Marchand F.: Weak-strong uniqueness criteria for the critical quasi-geostrophic equation. Phys. D 237, 1346-1351 (2008).
    • (2008) Phys. D , vol.237 , pp. 1346-1351
    • Marchand, F.1
  • 66
    • 27744501518 scopus 로고    scopus 로고
    • Solutions auto-similaires non radiales pour l'équation quasi-géostrophique dissipative critique
    • Marchand F., Lemarié-Rieusset P. G.: Solutions auto-similaires non radiales pour l'équation quasi-géostrophique dissipative critique. C. R. Math. Acad. Sci. Paris 341, 535-538 (2005).
    • (2005) C. R. Math. Acad. Sci. Paris , vol.341 , pp. 535-538
    • Marchand, F.1    Lemarié-Rieusset, P.G.2
  • 68
    • 80052418263 scopus 로고    scopus 로고
    • arXiv: 0910. 0998v1. 6 Oct
    • 1. arXiv: 0910. 0998v1. 6 Oct 2009.
    • (2009) 1
    • May, R.1
  • 69
    • 48349135452 scopus 로고    scopus 로고
    • Global existence of solutions for subcritical quasi-geostrophic equations
    • May R., Zahrouni E.: Global existence of solutions for subcritical quasi-geostrophic equations. Commun. Pure Appl. Anal. 7, 1179-1191 (2008).
    • (2008) Commun. Pure Appl. Anal. , vol.7 , pp. 1179-1191
    • May, R.1    Zahrouni, E.2
  • 71
    • 33747198457 scopus 로고    scopus 로고
    • Dissipative quasi-geostrophic equation for large initial data in the critical sobolev space
    • Miura H.: Dissipative quasi-geostrophic equation for large initial data in the critical sobolev space. Commun. Math. Phys. 267, 141-157 (2006).
    • (2006) Commun. Math. Phys. , vol.267 , pp. 141-157
    • Miura, H.1
  • 72
    • 34848865949 scopus 로고    scopus 로고
    • Decay of weak solutions to the 2D dissipative quasi-geostrophic equation
    • Niche C., Schonbek M.: Decay of weak solutions to the 2D dissipative quasi-geostrophic equation. Commun. Math. Phys. 276, 93-115 (2007).
    • (2007) Commun. Math. Phys. , vol.276 , pp. 93-115
    • Niche, C.1    Schonbek, M.2
  • 73
    • 0030876020 scopus 로고    scopus 로고
    • Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow
    • Ohkitani K., Yamada M.: Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow. Phys. Fluids 9, 876-882 (1997).
    • (1997) Phys. Fluids , vol.9 , pp. 876-882
    • Ohkitani, K.1    Yamada, M.2
  • 75
    • 76349094273 scopus 로고    scopus 로고
    • Destructive interactions between two counter-rotating quasi-geostrophic vortices
    • Reinaud J., Dritschel D.: Destructive interactions between two counter-rotating quasi-geostrophic vortices. J. Fluid Mech. 639, 195-211 (2009).
    • (2009) J. Fluid Mech. , vol.639 , pp. 195-211
    • Reinaud, J.1    Dritschel, D.2
  • 77
    • 1542327711 scopus 로고    scopus 로고
    • The vortex patch problem for the surface quasi-geostrophic equation
    • Rodrigo J.: The vortex patch problem for the surface quasi-geostrophic equation. Proc. Natl. Acad. Sci. USA 101, 2684-2686 (2004).
    • (2004) Proc. Natl. Acad. Sci. USA , vol.101 , pp. 2684-2686
    • Rodrigo, J.1
  • 78
    • 17844372561 scopus 로고    scopus 로고
    • On the evolution of sharp fronts for the quasi-geostrophic equation
    • Rodrigo J.: On the evolution of sharp fronts for the quasi-geostrophic equation. Commun. Pure Appl. Math. 58, 821-866 (2005).
    • (2005) Commun. Pure Appl. Math. , vol.58 , pp. 821-866
    • Rodrigo, J.1
  • 79
    • 1642618627 scopus 로고    scopus 로고
    • Asymptotic behavior to dissipative quasi-geostrophic flows
    • Schonbek M., Schonbek T.: Asymptotic behavior to dissipative quasi-geostrophic flows. SIAM J. Math. Anal. 35, 357-375 (2003).
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 357-375
    • Schonbek, M.1    Schonbek, T.2
  • 80
    • 28444450853 scopus 로고    scopus 로고
    • Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows
    • Schonbek M., Schonbek T.: Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows. Discrete Contin. Dyn. Syst. 13, 1277-1304 (2005).
    • (2005) Discrete Contin. Dyn. Syst. , vol.13 , pp. 1277-1304
    • Schonbek, M.1    Schonbek, T.2
  • 81
    • 76849110369 scopus 로고    scopus 로고
    • Eventual regularization for the slightly supercritical quasi-geostrophic equation
    • Silvestre L.: Eventual regularization for the slightly supercritical quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 27(2), 693-704 (2010).
    • (2010) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.27 , Issue.2 , pp. 693-704
    • Silvestre, L.1
  • 83
    • 36849031175 scopus 로고    scopus 로고
    • Global well-posedness for the 2D quasi-geostrophic equation in a critical Besov space
    • Stefanov A.: Global well-posedness for the 2D quasi-geostrophic equation in a critical Besov space. Electron. J. Differ. Equ. 2007.
    • (2007) Electron. J. Differ. Equ
    • Stefanov, A.1
  • 85
    • 0004058897 scopus 로고
    • Monographs in Mathematics, Basel: Birkhauser
    • Triebel H.: Theory of Function Spaces, Monographs in Mathematics Vol. 78. Birkhauser, Basel (1983).
    • (1983) Theory of Function Spaces , vol.78
    • Triebel, H.1
  • 86
    • 62949113276 scopus 로고    scopus 로고
    • Local well-posedness for the 2D non-dissipative quasi-geostrophicequation in Besov spaces
    • Wang H., Jia H.: Local well-posedness for the 2D non-dissipative quasi-geostrophic equation in Besov spaces. Nonlinear Anal. 70, 3791-3798 (2009).
    • (2009) Nonlinear Anal. , vol.70 , pp. 3791-3798
    • Wang, H.1    Jia, H.2
  • 87
    • 0001139624 scopus 로고    scopus 로고
    • Quasi-geostrophic-type equations with initial data in Morrey spaces
    • Wu J.: Quasi-geostrophic-type equations with initial data in Morrey spaces. Nonlinearity 10, 1409-1420 (1997).
    • (1997) Nonlinearity , vol.10 , pp. 1409-1420
    • Wu, J.1
  • 88
    • 0000601689 scopus 로고    scopus 로고
    • Inviscid limits and regularity estimates for the solutions of the 2-D dissipative quasi-geostrophic equations
    • Wu J.: Inviscid limits and regularity estimates for the solutions of the 2-D dissipative quasi-geostrophic equations. Indiana Univ. Math. J. 46, 1113-1124 (1997).
    • (1997) Indiana Univ. Math. J. , vol.46 , pp. 1113-1124
    • Wu, J.1
  • 90
    • 0036381898 scopus 로고    scopus 로고
    • The quasi-geostrophic equation and its two regularizations
    • Wu J.: The quasi-geostrophic equation and its two regularizations. Commun. Partial Differ. Equ. 27, 1161-1181 (2002).
    • (2002) Commun. Partial Differ. Equ. , vol.27 , pp. 1161-1181
    • Wu, J.1
  • 91
    • 18744399570 scopus 로고    scopus 로고
    • Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces
    • Wu J.: Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces. SIAM J. Math. Anal. 36, 1014-1030 (2004/2005).
    • (2004) SIAM J. Math. Anal , vol.36 , pp. 1014-1030
    • Wu, J.1
  • 92
    • 11844291951 scopus 로고    scopus 로고
    • The quasi-geostrophic equation with critical or supercritical dissipation
    • Wu J.: The quasi-geostrophic equation with critical or supercritical dissipation. Nonlinearity 18, 139-154 (2005).
    • (2005) Nonlinearity , vol.18 , pp. 139-154
    • Wu, J.1
  • 93
    • 20444469300 scopus 로고    scopus 로고
    • Solutions of the 2-D quasi-geostrophic equation in Hölder spaces
    • Wu J.: Solutions of the 2-D quasi-geostrophic equation in Hölder spaces. Nonlinear Analysis 62, 579-594 (2005).
    • (2005) Nonlinear Analysis , vol.62 , pp. 579-594
    • Wu, J.1
  • 94
    • 33645305133 scopus 로고    scopus 로고
    • Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
    • Wu J.: Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces. Commun. Math. Phys. 263, 803-831 (2006).
    • (2006) Commun. Math. Phys. , vol.263 , pp. 803-831
    • Wu, J.1
  • 95
    • 34547513199 scopus 로고    scopus 로고
    • Existence and uniqueness results for the 2-D dissipative quasi-geostrophic equation
    • Wu J.: Existence and uniqueness results for the 2-D dissipative quasi-geostrophic equation. Nonlinear Anal. 67, 3013-3036 (2007).
    • (2007) Nonlinear Anal. , vol.67 , pp. 3013-3036
    • Wu, J.1
  • 96
    • 35248823548 scopus 로고    scopus 로고
    • Remarks on the global regularity for the super-critical 2D dissipative quasi-geostrophic equation
    • Yu X.: Remarks on the global regularity for the super-critical 2D dissipative quasi-geostrophic equation. J. Math. Anal. Appl. 339, 359-371 (2008).
    • (2008) J. Math. Anal. Appl. , vol.339 , pp. 359-371
    • Yu, X.1
  • 97
    • 40549112019 scopus 로고    scopus 로고
    • The dissipative quasi-geostrophic equation in weak Morrey spaces
    • Yuan B.: The dissipative quasi-geostrophic equation in weak Morrey spaces. Acta Math. Sin. (Engl. Ser.) 24, 253-266 (2008).
    • (2008) Acta Math. Sin. (Engl. Ser.) , vol.24 , pp. 253-266
    • Yuan, B.1
  • 98
    • 37449010374 scopus 로고    scopus 로고
    • On regularity criterion for the dissipative quasi-geostrophic equations
    • Yuan J.: On regularity criterion for the dissipative quasi-geostrophic equations. J. Math. Anal. Appl. 340, 334-339 (2008).
    • (2008) J. Math. Anal. Appl. , vol.340 , pp. 334-339
    • Yuan, J.1
  • 99
    • 29144449430 scopus 로고    scopus 로고
    • Well-posedness for the 2D dissipative quasi-geostrophic equations in the Besov space
    • Zhang Z.: Well-posedness for the 2D dissipative quasi-geostrophic equations in the Besov space. Sci. China Ser. A 48, 1646-1655 (2005).
    • (2005) Sci. China Ser. A , vol.48 , pp. 1646-1655
    • Zhang, Z.1
  • 100
    • 34547244974 scopus 로고    scopus 로고
    • Global well-posedness for the 2D critical dissipative quasi-geostrophic equation
    • Zhang Z.: Global well-posedness for the 2D critical dissipative quasi-geostrophic equation. Sci. China Ser. A 50, 485-494 (2007).
    • (2007) Sci. China Ser. A , vol.50 , pp. 485-494
    • Zhang, Z.1
  • 101
    • 33644499492 scopus 로고    scopus 로고
    • Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows
    • Zhou Y.: Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows. Discrete Contin. Dyn. Syst. 14, 525-532 (2006).
    • (2006) Discrete Contin. Dyn. Syst. , vol.14 , pp. 525-532
    • Zhou, Y.1
  • 102
    • 52049107343 scopus 로고    scopus 로고
    • Asymptotic behaviour of the solutions to the 2D dissipative quasi-geostrophic flows
    • Zhou Y.: Asymptotic behaviour of the solutions to the 2D dissipative quasi-geostrophic flows. Nonlinearity 21, 2061-2071 (2008).
    • (2008) Nonlinearity , vol.21 , pp. 2061-2071
    • Zhou, Y.1


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