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On the improved regularity criterion of the solutions to the Navier-Stokes equations

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This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.

Abstract

This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.

참고문헌 (24)

  1. C. H. Chan, "Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations", Methods Appl. Anal., 14(2), pp.197~212 (2007)[DOI]
  2. B. Dong, "On the regularity criteria of the 3D Navier-Stokes equations in critical spaces", Acta Math. Sci. Ser. B (Engl. Ed.), 31(2), pp.591~600 (2011)[DOI]
  3. J. Fan, "On logarithmically improved regularity criteria for the Navier-Stokes equations in Rn", IMA J. Appl. Math., 76(2), pp.298~311 (2011)[DOI]
  4. J. Fan, "Logarithmically improved regularity criteria for the Navier-Stokes and MHD equations", J. Math. Fluid Mech., 13(4), pp.557~571 (2011)[DOI]
  5. J. Fan, "On regularity criteria for the n-dimensional Navier-Stokes equations in terms of the pressure", J. Differential Equations, 244(11), pp.2963~2979 (2008)[DOI]
  6. J. Fan, "Regularity criterion for weak solutions to the Navier-Stokes equations in terms of the gradient of the pressure", J. Inequal. Appl, 2008, pp.412678~412683 (2008)[DOI]
  7. J. Fan, "Logarithmically improved regularity criteria for Navier-Stokes and related equations", Math. Methods Appl. Sci, 32(17), pp.2309~2318 (2009)[DOI]
  8. Sadek Gala, "Regularity criterion on weak solutions to the Navier-Stokes equations", 대한수학회지, 45(2), pp.537~558 (2008), 대한수학회
  9. S. Gala, "Remark on a regularity criterion in terms of pressure for the Navier-Stokes equations", Quart. Appl. Math, 69(1), pp.147~155 (2011)
  10. S. Gala, "A remark on the blow-up criterion of strong solutions to the Navier-Stokes equations", Appl. Math. Comput., 217(22), pp.9488~9491 (2011)[DOI]
  11. S. Gala, "Remarks on regularity criterion for weak solutions to the Navier-Stokes equations in terms of the gradient of the pressure", Appl. Anal, 92(1), pp.96~103 (2013)[DOI]
  12. P. Gerard, "Oru, Inegalites de Sobolev precisees", Seminaire sur les Equations aux Derivees Partielles, 1996-1997, Exp. IV, pp.11~ (1997), Ecole Polytech
  13. X. He, "Regularity criterion for weak solutions to the Navier-Stokes equations in terms of the pressure in the class L2(0, T, B -1∞,∞(R3))", Nonlinear Anal, 12, pp.3602~3607 (2011)
  14. E. Hopf, "Uber die Anfangswertaufgabe fur die hydrodynamischen Grundgleichungen", Math. Nachr, 4, pp.213~231 (1951)[DOI]
  15. J. Leray, "Sur le mouvement d'un liquide visqueux emplissant l'espace", Acta Math, 63(1), pp.193~248 (1934)[DOI]
  16. J. Serrin, "On the interior regularity of weak solutions of the Navier-Stokes equations", Arch. Rational Mech. Anal, 9, pp.187~195 (1962)[DOI]
  17. M. Struwe, "On partial regularity results for the Navier-Stokes equations", Comm. Pure Appl. Math., 41(4), pp.437~458 (1988)[DOI]
  18. Y. Zhou, "On regularity criteria in terms of pressure for the Navier-Stokes equations in R3", Proc. Amer. Math. Soc, 134(1), pp.149~156 (2006)[DOI]
  19. Y. Zhou, "On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in RN", Z. Angew. Math. Phys., 57(3), pp.384~392 (2006)[DOI]
  20. Y. Zhou, "Logarithmically improved regularity criteria for the 3D viscous MHD equations", Forum Math., 24(4), pp.691~708 (2012)[DOI]
  21. Y. Zhou, "Logarithmically improved regularity criteria for the Navier-Stokes equations in multiplier spaces", J. Math. Anal. Appl., 356(2), pp.498~501 (2009)[DOI]
  22. Y. Zhou, "Regularity criteria in terms of the pressure for the Navier-Stokes equations in the critical Morrey-Campanato space", Z. Anal. Anwend., 30(1), pp.83~93 (2011)[DOI]
  23. Y. Zhou, "Remarks on logarithmical regularity criteria for the Navier-Stokes equations", J. Math. Phys., 52(6), pp.063503~063511 (2011)[DOI]
  24. Y. Zhou, "Logarithmically improved criteria for Euler and Navier-Stokes equations", Commun. Pure Appl. Anal., 12(6), pp.2715~2719 (2013)[DOI]

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