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arXiv · 1111.6760

A Beale--Kato--Majda criterion for the 3-D Compressible Nematic Liquid Crystal Flows with Vacuum

Qiao Liu·Shangbin Cui
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Abstract

In this paper, we prove a Beale--Kato--Majda blow-up criterion in terms of the gradient of the velocity only for the strong solution to the 3-D compressible nematic liquid crystal flows with nonnegative initial densities. More precisely, the strong solution exists globally if the $L^{1}(0,T;L^{\infty})$-norm of the gradient of the velocity $u$ is bounded. Our criterion improves the recent result of X. Liu and L. Liu (\cite{LL}, A blow-up criterion for the compressible liquid crystals system, arXiv:1011.4399v2 [math-ph] 23 Nov. 2010).

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Qiao Liu, Shangbin Cui. 2011-11-29. A Beale--Kato--Majda criterion for the 3-D Compressible Nematic Liquid Crystal Flows with Vacuum. https://arxiv.org/abs/1111.6760

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