Asymptotic Behavior of Solutions to the Liquid Crystal System in $H^m({\mathbb{R}}^3)$

Abstract

In this paper we study the large time behavior of regular solutions to a nematic liquid crystal system in Sobolev spaces $H^m({\mathbb{R}}^3)$ for $m\ge 0$.We obtain optimal decay rates in $H^m(R^3)$ spaces, in the sense that the rates coincide with the rates of the underlying linear counterpart. The fluid under consideration has constant density and small initial data.

21 pages