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2014 | 12 | 7 | 1015-1025
Tytuł artykułu

A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
7
Strony
1015-1025
Opis fizyczny
Daty
wydano
2014-07-01
online
2014-04-03
Twórcy
autor
Bibliografia
  • [1] Beirão da Veiga H., Remarks on the smoothness of the L ∞(0, T, L 3) solutions of the 3-D Navier-Stokes equations, Portugal. Math., 1997, 54(4), 381–391
  • [2] Berselli L.C., Galdi G.P., Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations, Proc. Amer. Math. Soc., 2002, 130(12), 3585–3595 http://dx.doi.org/10.1090/S0002-9939-02-06697-2
  • [3] Bjorland C., Vasseur A., Weak in space, log in time improvement of the Ladyženskaja-Prodi-Serrin criteria, J. Math. Fluid Mech., 2011, 13(2), 259–269 http://dx.doi.org/10.1007/s00021-009-0020-3
  • [4] Caffarelli L., Kohn R., Nirenberg L., Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math., 1982, 35(6), 771–831 http://dx.doi.org/10.1002/cpa.3160350604
  • [5] Cai Z., Fan J., Zhai J., Regularity criteria in weak spaces for 3-dimensional Navier-Stokes equations in terms of the pressure, Differential Integral Equations, 2010, 23(11–12), 1023–1033
  • [6] Chan C.H., Vasseur A., Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations, Methods Appl. Anal., 2007, 14(2), 197–212
  • [7] Escauriaza L., Seregin G., Šverák V., L 3,∞-solutions of the Navier-Stokes equations and backward uniqueness, Russian Math. Surveys, 2003, 58(2), 211–250 http://dx.doi.org/10.1070/RM2003v058n02ABEH000609
  • [8] Fan J., Jiang S., Ni G., On regularity criteria for the n-dimensional Navier-Stokes equations in terms of the pressure, J. Differential Equations, 2008, 244(11), 2963–2979 http://dx.doi.org/10.1016/j.jde.2008.02.030
  • [9] Giga Y., Solutions for semilinear parabolic equations in L p and regularity of weak solutions of the Navier-Stokes equations, J. Differential Equations, 1986, 62(2), 186–212 http://dx.doi.org/10.1016/0022-0396(86)90096-3
  • [10] Hopf E., Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., 1951, 4, 213–231 http://dx.doi.org/10.1002/mana.3210040121
  • [11] Leray J., Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math., 1934, 63, 193–248 http://dx.doi.org/10.1007/BF02547354
  • [12] Montgomery-Smith S., Conditions implying regularity of the three dimensional Navier-Stokes equation, Appl. Math., 2005, 50(5), 451–464 http://dx.doi.org/10.1007/s10492-005-0032-0
  • [13] Pata V., On the regularity of solutions to the Navier-Stokes equations, Commun. Pure Appl. Anal., 2012, 11(2), 747–761 http://dx.doi.org/10.3934/cpaa.2012.11.747
  • [14] Prodi G., Un teorema di unicità per le equazioni di Navier-Stokes, Ann. Mat. Pura Appl., 1959, 48, 173–182 http://dx.doi.org/10.1007/BF02410664
  • [15] Serrin J., On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 1962, 9, 187–195 http://dx.doi.org/10.1007/BF00253344
  • [16] Sohr H., A regularity class for the Navier-Stokes equations in Lorentz spaces, J. Evol. Equ., 2001, 1(4), 441–467 http://dx.doi.org/10.1007/PL00001382
  • [17] Struwe M., On partial regularity results for the Navier-Stokes equations, Comm. Pure Appl. Math., 1988, 41(4), 437–458 http://dx.doi.org/10.1002/cpa.3160410404
  • [18] Struwe M., On a Serrin-type regularity criterion for the Navier-Stokes equations in terms of the pressure, J. Math. Fluid Mech., 2007, 9(2), 235–242 http://dx.doi.org/10.1007/s00021-005-0198-y
  • [19] Suzuki T., Regularity criteria of weak solutions in terms of the pressure in Lorentz spaces to the Navier-Stokes equations, J. Math. Fluid Mech., 2012, 14(4), 653–660 http://dx.doi.org/10.1007/s00021-012-0098-x
  • [20] Takahashi S., On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscripta Math., 1990, 69(3), 237–254 http://dx.doi.org/10.1007/BF02567922
  • [21] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl., 1976, 110, 353–372 http://dx.doi.org/10.1007/BF02418013
  • [22] Temam R., Navier-Stokes Equations, AMS Chelsea, Providence, 2001
  • [23] Zhou Y., On regularity criteria in terms of pressure for the Navier-Stokes equations in ℝ3, Proc. Amer. Math. Soc., 2006, 134(1), 149–156 http://dx.doi.org/10.1090/S0002-9939-05-08312-7
  • [24] Zhou Y., On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in ℝN, Z. Angew. Math. Phys., 2006, 57(3), 384–392 http://dx.doi.org/10.1007/s00033-005-0021-x
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0395-5
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