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In this paper, we establish the regularity criterion for the weak solution of nematic liquid crystal flows in three dimensions when the L ∞ ( 0 , T ; B ˙ ∞ , ∞ − 1 ) $L^{\infty }(0,T;\dot{B}_{\infty,\infty }^{-1})$ -norm of a suitable low frequency part of ( u , ∇ d ) $(u,\nabla d)$ is bounded by a scaling invariant constant and the initial data ( u 0 , ∇ d 0 ) $(u_{0},\nabla d_{0})$ . 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 ).

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