Long-time behavior of solution for the compressible nematic liquid crystal flows in R3

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Gao, Jincheng¹  Tao, Qiang²  Yao, Zheng-an¹ 

[1] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

[2] Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Peoples R China

关键词: Compressible nematic liquid crystal flows;    Global solution;    Long-time behavior;    Fourier splitting method;   

DOI  :  10.1016/j.jde.2016.04.033

来源: Elsevier

【 摘 要 】

In this paper, we investigate the global existence and long-time behavior of classical solution for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in H-N (R-3) (N >= 3)-framework. Then, one establishes algebraic time decay for the classical solution by weighted energy method. Finally, the algebraic decay rate of classical solution in L-P (R-3)-norm with 2 <= p <= infinity and optimal decay rate of their spatial derivative in L-2 (R-3)-norm are obtained if the initial perturbation belong to L-1(R-3) additionally. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free