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

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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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