AIMS Mathematics, 2020, 5(1): 619-628. doi: 10.3934/math.2020041

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Blow-up criterion for the 3D nematic liquid crystal flows via one velocity and vorticity components and molecular orientations

School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, China

In this paper, we are devoted to investigating the blow-up criteria for the three dimensionalnematic liquid crystal flows. More precisely, we proved that the smoothsolution $(u,d)$ can be extended beyond T, provided that $\int_{0}^{T}(||\omega_{3}||_{L^{p}}^{\frac{2p}{2p-3}}+||u_{3}||_{L^{q}}^{\frac{2q}{q-3}}+||\nabla d||_{\dot{B}_{\infty,\infty}^{0}}^{2})d t<\infty, \frac{3}{2}<p\leq\infty, 3<q\leq\infty.$
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