Remarks on the regularity criterion for the nematic liquid crystal flows in R3

摘要

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 ∂iu,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.