Long-time Behavior of Solution for the Compressible Nematic Liquid Crystal Flows in ℝ³

2015/03/10 by Jincheng Gao, Gao, Jincheng, Qiang Tao +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1503.02865

openalex publication_date 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the Cauchy problem for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the time decay rates for compressible nematic liquid crystal flows by the method of spectral analysis and energy estimates. Furthermore, we enhance the convergence rates for the higher-order spatial derivatives of density, velocity and director. Finally, the time decay rates of mixed space-time derivatives of solution are also established.

Citations

• Some constitutive equations for liquid crystals

Related

• Asymptotic Behavior of Solution to the Incompressible Nematic Liquid Crystal Flows in R³
• The Optimal Decay Rate of Strong Solution for the Compressible Nematic Liquid Crystal Equations with Large Initial Data
• Global well-posedness and large time behavior for compressible non-isothermal nematic liquid crystal flows with vacuum at infinity
• Time decay rate of global strong solutions to nematic liquid crystal flows in \mathbb R³₊
• Uniform Regularity and Vanishing Viscosity Limit for the Compressible Nematic Liquid Crystal Flows in Three Dimensional Bounded Domain