A regularity criterion via horizontal components of velocity and molecular orientations for the 3D nematic liquid crystal flows

Qiang Li; Mianlu Zou; Qiang Li; Mianlu Zou

doi:10.3934/math.2022514

AIMS Mathematics

2022, Volume 7, Issue 5: 9278-9287. doi: 10.3934/math.2022514

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Research article

A regularity criterion via horizontal components of velocity and molecular orientations for the 3D nematic liquid crystal flows

Qiang Li ^{1
,
,},
Mianlu Zou ²

1.
School of Mathematics and Statistics, Xinyang College, Henan 464000, China
2.
School of Big Data and Artificial Intelligence, Xinyang College, Henan 464000, China

Received: 07 January 2022 Revised: 19 February 2022 Accepted: 04 March 2022 Published: 09 March 2022
MSC : 35B65, 35Q35, 76A15

In this paper, we obtain a regularity criterion via horizontal components of velocity and molecular orientations for the 3D nematic liquid crystal flows. That is the smooth solution $ (u, d) $ can be extended beyond T, provided that $ \int_{0}^{T}(||u_{h}||_{\dot{B}_{\infty, \infty}^{0}}^{2}+||\nabla d||_{\dot{B}_{\infty, \infty}^{0}}^{2}) \mbox{d} t < \infty $.
- nematic liquid crystal flows,
- Navier-Stokes equations,
- regularity criterion
Citation: Qiang Li, Mianlu Zou. A regularity criterion via horizontal components of velocity and molecular orientations for the 3D nematic liquid crystal flows[J]. AIMS Mathematics, 2022, 7(5): 9278-9287. doi: 10.3934/math.2022514

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Abstract

In this paper, we obtain a regularity criterion via horizontal components of velocity and molecular orientations for the 3D nematic liquid crystal flows. That is the smooth solution $ (u, d) $ can be extended beyond T, provided that $ \int_{0}^{T}(||u_{h}||_{\dot{B}_{\infty, \infty}^{0}}^{2}+||\nabla d||_{\dot{B}_{\infty, \infty}^{0}}^{2}) \mbox{d} t < \infty $.

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