Regularity criterion for 3D nematic liquid crystal flows in terms of finite frequency parts in dot{B}_{infty,infty }^{-1}

Abstract

In this paper, we establish the regularity criterion for the weak solution of nematic liquid crystal flows in three dimensions when the L^{infty }(0,T;dot{B}_{infty,infty }^{-1})-norm of a suitable low frequency part of (u,nabla d) is bounded by a scaling invariant constant and the initial data (u_{0},nabla d_{0}). Our result refines the corresponding one in (Liu and Zhao in J. Math. Anal. Appl. 407:557-566, 2013) and that in (Ri in Nonlinear Anal. TMA 190:111619, 2020).