Limiting case for the regularity criterion of the Navier-Stokes equations and the magnetohydrodynamic equations

被引：11

作者：

He Cheng ^{[1
]}

Wang Yun ^{[2
,3
]}

机构：

[1] Natl Nat Sci Fdn China, Dept Math & Phys Sci, Div Math, Beijing 100085, Peoples R China

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[3] Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2010年 / 53卷 / 07期

关键词：

Navier-Stokes equations; magnetohydrodynamics equations; regularity criterion; MAGNETO-HYDRODYNAMICS EQUATIONS; 3D MHD EQUATIONS; WEAK SOLUTIONS; INTERIOR REGULARITY; SPACES; LP;

D O I：

10.1007/s11425-010-3135-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u||(Lw2(0,T;L infinity(R3))) is sufficiently small, which is a limiting case of the regularity criteria derived by Kim and Kozono. Our result gives a positive answer to the question proposed by Kim and Kozono. For the incompressible magnetohydrodynamic equations, we also show the regularity of weak solution only under the assumption that ||u||(Lw2(0,T;L infinity(R3))) is sufficiently small.

引用

页码：1767 / 1774

页数：8

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