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).

中文翻译：

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根据\（\ dot {B} _ {\ infty，\ infty} ^ {-1} \）中有限频率部分的3D向列液晶流的规则性准则

在本文中，我们建立了当$ L ^ {\ infty}（0，T; \ dot {B} _ {\ infty，\ infty} ^ { -1}）$-$（u，\ nabla d）$的适当低频部分的范数以缩放不变常数和初始数据$（u_ {0}，\ nabla d_ {0}）$为界。我们的结果完善了（Liu和Zhao在J. Math。Anal。Appl。407：557-566，2013）和（Ri in Nonlinear Anal。TMA 190：111619，2020）中的对应项。