In this paper, we investigate the regularity criteria for the 3D nematic liquid crystal flows in terms of the components of the velocity u or the gradient of the velocity field ?u. More precisely, the anisotropic integrability regularity criterion to the 3D nematic liquid crystal flows involving ? i u , i = 1 , 2 , 3 is obtained firstly, and then it is proved that the solution is regular if u3, ω3 or ?3u3, ω3 satisfies the Prodi-Serrin type conditions.
['Chenyin Qian']
Remarks on the regularity criterion for the nematic liquid crystal flows in R 3