看一点

Navier-Stokes equations

Magnetohydrodynamic equations

Micropolar fluid equations

[B.Q. Dong, W.L. Zhang, On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces, Nonlinear Anal., 73 (2010), 2334--2341]: $$\bee\label{Dong_Zhang_10_NA} \bbu\in L^\frac{2}{1+r}(0,T;B^r_{\infty,\infty}),\quad -1<r<1. \eee$$Main idea: Fourier localization technique and Bony‘s para-product decomposition.

Liquid Crystals