Two regularity criteria for the 3D MHD equations

被引：258
作者：
Cao, Chongsheng [2 ]
Wu, Jiahong [1 ]
机构：
[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA
[2] Florida Int Univ, Dept Math, Miami, FL 33199 USA
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 248卷 / 09期
基金：
美国国家科学基金会;
关键词：
3D MHD equations; Regularity criteria; NAVIER-STOKES EQUATIONS; WEAK SOLUTIONS; WELL-POSEDNESS; HYDRODYNAMICS; PRESSURE; SINGULARITIES; INEQUALITIES; VORTICITY; EVOLUTION; BOUNDS;
D O I：
10.1016/j.jde.2009.09.020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：2263 / 2274
页数：12
相关论文
共 57 条
[1]  
Adams R., 1985, Sobolev Spaces
[2]   Non-uniform decay of MHD equations with and without magnetic diffusion [J].
Agapito, Ruben ;
Schonbek, Maria .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (10-12) :1791-1812
[3]  
[Anonymous], 2004, Applications of Mathematics
[4]  
[Anonymous], 1999, Electron. J. Differential Equations
[5]  
[Anonymous], 2002, Adv. Math. Sci. Appl
[6]  
[Anonymous], 1994, An introduction to the mathematical theory of the Navier-Stokes equations
[7]   REMARKS ON THE BREAKDOWN OF SMOOTH SOLUTIONS FOR THE 3-D EULER EQUATIONS [J].
BEALE, JT ;
KATO, T ;
MAJDA, A .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 94 (01) :61-66
[8]   Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations [J].
Berselli, LC ;
Galdi, GP .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (12) :3585-3595
[9]   Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD [J].
Caflisch, RE ;
Klapper, I ;
Steele, G .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 184 (02) :443-455
[10]  
CAO C, DISCRETE CO IN PRESS
123456