A remark on the logarithmically improved regularity criterion for the micropolar fluid equations in terms of the pressure

作者：Gala Sadek^*

来源：Mathematical Methods in the Applied Sciences, 2011, 34(16): 1945-1953.

DOI：10.1002/mma.1488

• Micropolar fluid equations
• regularity
• Besov spaces

In this paper, we study the regularity criterion of weak solutions of the three dimensional micropolar fluid flows. It is proved that if the pressure satisfies
integral(T)(0)parallel to pi(S,.)parallel to((2)(B)over dot infinity,infinity-1)/1+ln(e+parallel to pi(S,.)parallel to(L2))dswhere (B)over dot(infinity,infinity)(-1) denotes the critical Besov space, then the weak solution (u, w) becomes a regular solution on (0, T]. This regularity criterion can be regarded as log in time improvements of the standard Serrin's criteria established before.

• 出版日期2011-11-15