On Anisotropic Regularity Criteria for the Solutions to 3D Navier–Stokes Equations

被引：0
作者：
Patrick Penel
Milan Pokorný
机构：
[1] Université du Sud,Mathématique et labo. SNC
[2] Toulon-Var,undefined
[3] Mathematical Institute of Charles University,undefined
来源：
Journal of Mathematical Fluid Mechanics | 2011年 / 13卷
关键词：
Primary 35Q30; Secondary 76D05; Incompressible Navier–Stokes equations; regularity of solution; regularity criteria;
D O I：
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学科分类号：
摘要：
In this short note we consider the 3D Navier–Stokes equations in the whole space, for an incompressible fluid. We provide sufficient conditions for the regularity of strong solutions in terms of certain components of the velocity gradient. Based on the recent results from Kukavica (J Math Phys 48(6):065203, 2007) we show these conditions as anisotropic regularity criteria which partially interpolate results from Kukavica (J Math Phys 48(6):065203, 2007) and older results of similar type from Penel and Pokorný (Appl Math 49(5):483–493, 2004).
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页码：341 / 353
页数：12
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  • [1] Beirão da Veiga H.(1995)A new regularity class for the Navier–Stokes equations in Chin. Ann. Math. Ser. B 16 407-412
  • [2] Berselli L.(2002)Regularity criteria involving the pressure for the weak solutions to the Navier–Stokes equations Proc. Am. Math. Soc. 130 3585-3595
  • [3] Galdi G.P.(2008)Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643-2661
  • [4] Cao C.(1999)Regularity of solutions to the Navier–Stokes equation Electron. J. Differ. Equ. 5 1-7
  • [5] Titi E.S.(2003)Backward uniqueness for parabolic equations Arch. Ration. Mech. Anal. 169 147-157
  • [6] Chae D.(2007)Navier–Stokes equations with regularity in one direction J. Math. Phys. 48 10-469
  • [7] Choe H.J.(2006)One component regularity for the Navier–Stokes equations Nonlinearity 19 453-248
  • [8] Escauriaza L.(1934)Sur le mouvement d’un liquide visqueux emplissant l’espace Acta Math. 63 193-8
  • [9] Seregin G.(2003)On the result of He concerning the smoothness of solutions to the Navier–Stokes equations Electron. J. Differ. Equ. 11 1-182
  • [10] Šverák V.(1959)Un teorema di unicità per el equazioni di Navier–Stokes Ann. Mat. Pura Appl. IV 48 173-578
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