Regularity and uniqueness for a class of solutions to the hydrodynamic flow of nematic liquid crystals

In this paper, we establish an epsilon-regularity criterion for any weak solution (u, d) to the nematic liquid crystal flow (1.1) such that (u, del d) is an element of (LtLxq)-L-p for some p >= 2 and q >= n satisfying the condition (1.2). As consequences, we prove the interior smoothness of any such a solution when p > 2 and q > n. We also show that uniqueness holds for the class of weak solutions (u, d) the Cauchy problem of the nematic liquid crystal flow (1.1) that satisfy (u, del d). (LtLxq)-L-p for some p > 2 and q > n satisfying (1.2).