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

作　　者：He Cheng Wang Yun 

机构地区：[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

出　　处：《Science China Mathematics》2010年第7期1764-1771,共8页中国科学：数学（英文版）

基　　金：supported by the National Basic Research Program of China (973 Program) (Grant No. 2006CB805902);Knowledge Innovation Funds of Chinese Academy of Sciences (Grant No.KJCX3-SYW-S03)

摘　　要：Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) 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|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small.Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) 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|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small.

关 键 词：NAVIER-STOKES EQUATIONS MAGNETOHYDRODYNAMICS EQUATIONS REGULARITY criterion 

分 类 号：N[自然科学总论]