Global Existence and Long-Time Behavior for the Strong Solutions in $H^2$ to the 3D Compressible Nematic Liquid Crystal Flows
Year: 2016
Author: Jincheng Gao, Boling Guo, Xiaoyu Xi
Annals of Applied Mathematics, Vol. 32 (2016), Iss. 4 : pp. 331–356
Abstract
In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in three-dimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in $H^2$-framework. If the initial data in $L^1$-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-AAM-20648
Annals of Applied Mathematics, Vol. 32 (2016), Iss. 4 : pp. 331–356
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: compressible nematic liquid crystal flows global solution Green function long-time behavior.