On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces

This paper studies the regularity criterion of weak solutions for three-dimensional (3D) micropolar fluid flows. When the velocity field satisfies u is an element of L-2/(1+r) (0, T; B-infinity,infinity(r) (R-3)) FOR -1 < r < 1, then the weak solution (u,w) is regular on (0, T]. The methods are mainly based on the Fourier localization technique and Bony's para-product decomposition. (C) 2010 Elsevier Ltd. All rights reserved.