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Volumn 173, Issue 2, 2011, Pages 983-1012

Global regularity for some classes of large solutions to the Navier-Stokes equations

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EID: 79953220832     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2011.173.2.9     Document Type: Article
Times cited : (122)

References (36)
  • 1
    • 58049169062 scopus 로고    scopus 로고
    • Ill-posedness of the Navier-Stokes equations in a critical space in 3D
    • J. Bourgain and N. Pavlović, Ill-posedness of the Navier-Stokes equations in a critical space in 3D, J. Funct. Anal. 255 (2008), 2233-2247.
    • (2008) J. Funct. Anal. , vol.255 , pp. 2233-2247
    • Bourgain, J.1    Pavlović, N.2
  • 2
    • 62549111607 scopus 로고
    • Solutions auto-similaires des équations de Navier-Stokes
    • École Polytech., Palaiseau, 1993-1994, Exp. No. VIII
    • M. Cannone, Y. Meyer, and F. Planchon, Solutions auto-similaires des équations de Navier-Stokes, in Séminaire sur les Équations aux D́erivées Partielles, 1993-1994, École Polytech., Palaiseau, 1994, pp. Exp. No. VIII, 12.
    • (1994) Séminaire sur les Équations aux D́erivées Partielles , vol.8 , pp. 12
    • Cannone, M.1    Meyer, Y.2    Planchon, F.3
  • 5
    • 33846021612 scopus 로고    scopus 로고
    • On the global wellposedness of the 3-D Navier-Stokes equations with large initial data
    • J.-Y. Chemin and I. Gallagher, On the global wellposedness of the 3-D Navier-Stokes equations with large initial data, Ann. Sci. École Norm. Sup. 39 (2006), 679-698.
    • (2006) Ann. Sci. École Norm. Sup. , vol.39 , pp. 679-698
    • Chemin, J.-Y.1    Gallagher, I.2
  • 7
    • 77951630592 scopus 로고    scopus 로고
    • Large, global solutions to the Navier-Stokes equations, slowly varying in one direction
    • J.-Y. Chemin and I. Gallagher, Large, global solutions to the Navier-Stokes equations, slowly varying in one direction, Trans. Amer. Math. Soc. 362 (2010), 2859-2873.
    • (2010) Trans. Amer. Math. Soc. , vol.362 , pp. 2859-2873
    • Chemin, J.-Y.1    Gallagher, I.2
  • 8
    • 58149362915 scopus 로고
    • Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes
    • J.-Y. Chemin and N. Lerner, Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes, J. Differential Equations 121 (1995), 314-328.
    • (1995) J. Differential Equations , vol.121 , pp. 314-328
    • Chemin, J.-Y.1    Lerner, N.2
  • 9
    • 34247160971 scopus 로고    scopus 로고
    • On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations
    • J.-Y. Chemin and P. Zhang, On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations, Comm. Math. Phys. 272 (2007), 529-566.
    • (2007) Comm. Math. Phys. , vol.272 , pp. 529-566
    • Chemin, J.-Y.1    Zhang, P.2
  • 11
    • 34250947482 scopus 로고
    • On the Navier-Stokes initial value problem. I
    • H. Fujita and T. Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16 (1964), 269-315.
    • (1964) Arch. Rational Mech. Anal. , vol.16 , pp. 269-315
    • Fujita, H.1    Kato, T.2
  • 12
    • 1342347425 scopus 로고    scopus 로고
    • Asymptotics and stability for global solutions to the Navier-Stokes equations
    • Available at
    • I. Gallagher, D. Iftimie, and F. Planchon, Asymptotics and stability for global solutions to the Navier-Stokes equations, Ann. Inst. Fourier (Grenoble) 53 (2003), 1387-1424. Available at http://aif.cedram.org/item?id=AIF200353513870.
    • (2003) Ann. Inst. Fourier (Grenoble) , vol.53 , pp. 1387-1424
    • Gallagher, I.1    Iftimie, D.2    Planchon, F.3
  • 13
    • 77951079779 scopus 로고    scopus 로고
    • Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations
    • I. Gallagher and M. Paicu, Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations, Proc. Amer. Math. Soc. 137 (2009), 2075-2083.
    • (2009) Proc. Amer. Math. Soc. , vol.137 , pp. 2075-2083
    • Gallagher, I.1    Paicu, M.2
  • 14
    • 58049164748 scopus 로고    scopus 로고
    • The second iterate for the Navier-Stokes equation
    • P. Germain, The second iterate for the Navier-Stokes equation, J. Funct. Anal. 255 (2008), 2248-2264.
    • (2008) J. Funct. Anal. , vol.255 , pp. 2248-2264
    • Germain, P.1
  • 16
    • 0034403210 scopus 로고    scopus 로고
    • On the nonlinear instability of Euler and Prandtl equations
    • E. Grenier, On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math. 53 (2000), 1067-1091. MR 1761409. Zbl 1048.35081. doi: 10.1002/1097-0312(200009)53:9<1067::AID-CPA1>3.3.CO;2-H.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1067-1091
    • Grenier, E.1
  • 17
    • 0036436567 scopus 로고    scopus 로고
    • A uniqueness result for the Navier-Stokes equations with vanishing vertical viscosity
    • D. Iftimie, A uniqueness result for the Navier-Stokes equations with vanishing vertical viscosity, SIAM J. Math. Anal. 33 (2002), 1483-1493.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1483-1493
    • Iftimie, D.1
  • 18
    • 34547452104 scopus 로고    scopus 로고
    • Navier-Stokes equations in thin 3D domains with Navier boundary conditions
    • D. Iftimie, G. Raugel, and G. R. Sell, Navier-Stokes equations in thin 3D domains with Navier boundary conditions, Indiana Univ. Math. J. 56 (2007), 1083-1156.
    • (2007) Indiana Univ. Math. J. , vol.56 , pp. 1083-1156
    • Iftimie, D.1    Raugel, G.2    Sell, G.R.3
  • 19
    • 0000911759 scopus 로고
    • m, with applications to weak solutions
    • m, with applications to weak solutions, Math. Z. 187 (1984), 471-480.
    • (1984) Math. Z. , vol.187 , pp. 471-480
    • Kato, T.1
  • 20
    • 0035863969 scopus 로고    scopus 로고
    • Well-posedness for the Navier-Stokes equations
    • H. Koch and D. Tataru, Well-posedness for the Navier-Stokes equations, Adv. Math. 157 (2001), 22-35.
    • (2001) Adv. Math. , vol.157 , pp. 22-35
    • Koch, H.1    Tataru, D.2
  • 21
    • 17244378007 scopus 로고
    • The Mathematical Theory of Viscous Incompressible Flow
    • Gordon and Breach Science Publishers, New York, Second English edition, revised and enlarged. Translated from the Russian by Richard A. Silverman and John Chu
    • O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Math. Appl. 2, Gordon and Breach Science Publishers, New York, 1969, Second English edition, revised and enlarged. Translated from the Russian by Richard A. Silverman and John Chu.
    • (1969) Math. Appl. , vol.2
    • Ladyzhenskaya, O.A.1
  • 22
    • 33746011979 scopus 로고    scopus 로고
    • Recent Developments in the Navier-Stokes Problem
    • Chapman & Hall/CRC, Boca Raton, FL
    • P. G. Lemaríe-Rieusset, Recent Developments in the Navier-Stokes Problem, Chapman & Hall/CRC Research Notes in Math. 431, Chapman & Hall/CRC, Boca Raton, FL, 2002.
    • (2002) Chapman & Hall/CRC Research Notes in Math , vol.431
    • Lemaríe-Rieusset, P.G.1
  • 23
    • 0003068173 scopus 로고
    • Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
    • J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique, Journal Math. Pures et Appliquées 12 (1933), 1-82. Zbl 0006.16702.
    • (1933) Journal Math. Pures et Appliquées , vol.12 , pp. 1-82
    • Leray, J.1
  • 24
    • 51249193194 scopus 로고
    • Sur le mouvement d'un liquide visqueux emplissant l'espace
    • J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Matematica 63 (1933), 193-248.
    • (1933) Acta Matematica , vol.63 , pp. 193-248
    • Leray, J.1
  • 25
    • 77249155572 scopus 로고    scopus 로고
    • Instability of the Cauchy-Kovalevskaya solution for a class of non-linear systems
    • N. Lerner, Y. Morimoto, and C-J. Xu, Instability of the Cauchy-Kovalevskaya solution for a class of non-linear systems, Amer. J. Math. 132 (2010), 99-123.
    • (2010) Amer. J. Math. , vol.132 , pp. 99-123
    • Lerner, N.1    Morimoto, Y.2    Xu, C.-J.3
  • 26
    • 0001684396 scopus 로고
    • Invariant helical subspaces for the Navier-Stokes equations
    • A. Mahalov, E. S. Titi, and S. Leibovich, Invariant helical subspaces for the Navier-Stokes equations, Arch. Rational Mech. Anal. 112 (1990), 193-222.
    • (1990) Arch. Rational Mech. Anal. , vol.112 , pp. 193-222
    • Mahalov, A.1    Titi, E.S.2    Leibovich, S.3
  • 27
    • 33845990393 scopus 로고    scopus 로고
    • Global solvability of three-dimensional Navier-Stokes equations with uniformly high initial vorticity
    • A. S. Makhalov and V. P. Nikolaenko, Global solvability of three-dimensional Navier-Stokes equations with uniformly high initial vorticity, Us-pekhi Mat. Nauk 58 (2003), 79-110.
    • (2003) Us-pekhi Mat, Nauk , vol.58 , pp. 79-110
    • Makhalov, A.S.1    Nikolaenko, V.P.2
  • 28
    • 0010602596 scopus 로고    scopus 로고
    • Wavelets, paraproducts, and Navier-Stokes equations
    • International Press, Somerville, MA
    • Y. Meyer, Wavelets, paraproducts, and Navier-Stokes equations, in Current Developments in Mathematics, International Press, Somerville, MA, 1996, pp. 104-212.
    • (1996) Current Developments in Mathematics , pp. 104-212
    • Meyer, Y.1
  • 29
    • 23044529136 scopus 로고    scopus 로고
    • Finite time blow up for a Navier-Stokes like equation
    • S. Montgomery-Smith, Finite time blow up for a Navier-Stokes like equation, Proc. Amer. Math. Soc. 129 (2001), 3025-3029.
    • (2001) Proc. Amer. Math. Soc. , vol.129 , pp. 3025-3029
    • Montgomery-Smith, S.1
  • 30
    • 0001654863 scopus 로고    scopus 로고
    • On Leray's self-similar solutions of the Navier-Stokes equations
    • J. NeČas, M. Ruziçka, 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    Ruziçka, M.2    Šverák, V.3
  • 31
    • 21344460003 scopus 로고    scopus 로고
    • Équation anisotrope de Navier-Stokes dans des espaces critiques
    • Available at
    • M. Paicu, Équation anisotrope de Navier-Stokes dans des espaces critiques, Rev. Mat. Iberoamericana 21 (2005), 179-235. Available at http://projecteuclid.org/getRecord?id=euclid.rmi/1114176232.
    • (2005) Rev. Mat. Iberoamericana , vol.21 , pp. 179-235
    • Paicu, M.1
  • 32
    • 21344484568 scopus 로고
    • Global stability of large solutions to the 3D Navier-Stokes equations
    • Available at
    • G. Ponce, R. Racke, T. C. Sideris, and E. S. Titi, Global stability of large solutions to the 3D Navier-Stokes equations, Comm. Math. Phys. 159 (1994), 329-341. Available at http://projecteuclid.org/getRecord?id=euclid.cmp/1104254602.
    • (1994) Comm. Math. Phys. , vol.159 , pp. 329-341
    • Ponce, G.1    Racke, R.2    Sideris, T.C.3    Titi, E.S.4
  • 33
    • 84968467415 scopus 로고
    • Navier-Stokes equations on thin 3D domains. I. Global attractors and global regularity of solutions
    • G. Raugel and G. R. Sell, Navier-Stokes equations on thin 3D domains. I. Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993), 503-568.
    • (1993) J. Amer. Math. Soc. , vol.6 , pp. 503-568
    • Raugel, G.1    Sell, G.R.2
  • 34
    • 0032371860 scopus 로고    scopus 로고
    • Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations
    • M. Sammartino and R. E. Caflisch, Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations, Comm. Math. Phys. 192 (1998), 433-461.
    • (1998) Comm. Math. Phys. , vol.192 , pp. 433-461
    • Sammartino, M.1    Caflisch, R.E.2
  • 35
    • 49949123887 scopus 로고
    • Axially symmetric flows of ideal and viscous fluids filling the whole space
    • M. R. Ukhovskii and V. I. Iudovich, Axially symmetric flows of ideal and viscous fluids filling the whole space, J. Appl. Math. Mech. 32 (1968), 52-61.
    • (1968) J. Appl. Math. Mech. , vol.32 , pp. 52-61
    • Ukhovskii, M.R.1    Iudovich, V.I.2


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