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

Qiang Li; Baoquan Yuan

doi:10.3934/math.2020041

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

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

Qiang Li, Baoquan Yuan

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

Received: , Accepted: , Published:

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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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Keywords: nematic liquid crystal flow; blow-up criteria; smooth solution

Citation: Qiang Li, Baoquan Yuan. Blow-up criterion for the 3D nematic liquid crystal flows via one velocity and vorticity components and molecular orientations. AIMS Mathematics, 2020, 5(1): 619-628. doi: 10.3934/math.2020041

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This article has been cited by:

1. Qiang Li, Baoquan Yuan, Note on global regular solution to the 3D liquid crystal equations, Applied Mathematics Letters, 2020, 106491, 10.1016/j.aml.2020.106491

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