In this paper, we establish an $\epsilon$-regularity criterion for any weaksolution $(u,d)$ to the nematic liquid crystal flow (1.1) such that $(u,\nablad)\in L^p_tL^q_x$ for some $p\ge 2$ and $q\ge n$ satisfying the condition(1.2). As consequences, we prove the interior smoothness of any such a solutionwhen $p>2$ and $q>n$. We also show that uniqueness holds for the class of weaksolutions $(u,d)$ the Cauchy problem of the nematic liquid crystal flow (1.1)that satisfy $(u,\nabla d)\in L^p_tL^q_x$ for some $p>2$ and $q>n$ satisfying(1.2).
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机译：在本文中，我们为向列液晶流（1.1）的任何弱解$（u，d）$建立了一个\ epsilon $正则性准则，使得L ^ p_tL ^ q_x $中的$（u，\ nablad）\对于满足条件（1.2）的某些$ p \ ge 2 $和$ q \ ge n $。结果，我们证明了当$ p> 2 $和$ q> n $时，任何此类解决方案的内部光滑度。我们还表明，对于弱解$（u，d）$满足向列液晶流（1.1）的柯西问题，在某些情况下满足$（u，\ nabla d）\ L ^ p_tL ^ q_x $ $ p> 2 $和$ q> n $令人满意（1.2）。
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