A further note on the regularity criterion for the 3D nematic liquid crystal flows

Abstract

We give a further investigation on the regularity criteria for the 3D nematic liquid crystal flows. It is show that the obtained anisotropic integrability regularity criterion to the 3D nematic liquid crystal flows involving ∂iuj,i,j=1,2,3 is an improvement of Qian (2016). Besides, we also prove the solution is regular if some components of the velocity field and the vectorial field modeling the orientation of the crystal molecules satisfy the Prodi–Serrin type conditions.