A regularity criterion for the solution of the nematic liquid crystal flows in terms of B^-1_∞,∞-norm

2012/11/30 by Liu, Qiao, Zhao, Jihong
#35B65 #35Q35 #76A15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.7245

Abstract

In this paper, we investigate regularity criterion for the solution of the nematic liquid crystal flows in dimension three and two. We prove the solution (u,d) is smooth up to time T provided that there exists a positive constant ε₀>0 such that (i) for n=3, |(u,∇ d)|_L^∞(0,T;B^-1_∞,∞)≤ ε₀, and (ii) for n=2, |∇ d|_L^∞(0,T;B^-1_∞,∞)≤ ε₀.

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