Communications in Mathematical Sciences

Volume 13 (2015)

Number 8

Global strong solutions of the compressible nematic liquid crystal flow with the cylinder symmetry

Pages: 2065 – 2096

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n8.a5

Authors

Qiang Tao (College of Mathematics and Computational Science, Shenzhen University, China)

Jincheng Gao (School of Mathematics and Computational Science, Sun Yat-sen University, China)

Zheng-An Yao (School of Mathematics and Computational Science, Sun Yat-sen University, China)

Abstract

In this paper, we consider the well-posedness of the compressible nematic liquid crystal flow with the cylinder symmetry in $\mathbb{R}^3$. By establishing a uniform pointwise positive lower and upper bounds of the density, we derive the global existence and uniqueness of strong solution and show the long time behavior of the global solution. Our results do not need the smallness of the initial data. Furthermore, a regularity result of global strong solution is given as well.

Keywords

nematic liquid crystal flow, global strong solution, long time behavior, regularity

2010 Mathematics Subject Classification

35B40, 35Q35, 76N10

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Published 3 September 2015