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

2011/11/29 by Qiao Liu, Liu, Qiao, Shangbin Cui +1
Mathematics · #35B65 #35Q35 #76A15 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B65 #msc:35Q35 #msc:76A15 #msc:76N10

paper · pdf · doi:10.48550/arxiv.1111.6760

18pages

arxiv created 2011/11/29 · arxiv updated 2011/11/30

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 L¹(0,T;L^∞)-norm of the gradient of the velocity u is bounded. Our criterion improves the recent result of X. Liu and L. Liu (\citeLL, A blow-up criterion for the compressible liquid crystals system, arXiv:1011.4399v2 [math-ph] 23 Nov. 2010).

Citations

• A blow-up criterion for the compressible liquid crystals system

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