Abstract
In this paper, we derive two regularity criteria of solutions to the
nematic liquid crystal flows. More precisely, we prove the local smooth
solution $(u, d)$ is regular if and only if one of the following two
conditions is satisfied: (i) $\nabla_{h}
u_{h}\in
L^{\frac{2p}{2p-3}}(0,T;
L^{p}(\mathbb{R}^{3})),\
\partial_{3} d\in
L^{\frac{2q}{q-3}}(0,T;
L^{q}(\mathbb{R}^{3})),\
\frac{3}{2}<
p\leq\infty,\ 3<
q\leq\infty$; and (ii)
$\nabla_{h} u_{h}\in
L^{q}(0,T;
L^{p}(\mathbb{R}^{3})),\
\frac{3}{p}+\frac{2}{q}\leq
1, \ 3
