Asymptotic Behavior of Solution to the Incompressible Nematic Liquid Crystal Flows in R^3

Abstract

In this paper, we investigate the Cauchy problem for the incompressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the global existence of solution by energy method under assumption of small initial data. Furthermore, the time decay rates of velocity and director are built when the initial data belongs to $L^1({\mathbb{R}}^3)$ additionally. Finally, one also constructs the time convergence rates for the mixed space-time derivatives of velocity and director.

arXiv comment26 pages

References in corpus (5)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain
• Global existence of weak solutions of the nematic liquid crystal flow in dimensions three
• Global Strong Solutions to Incompressible Nematic Liquid Crystal Flow
• Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three