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

Mimi Dai, Maria E. Schonbek

Published 2012-08-15, updated 2012-10-11Version 2

In this paper we study the large time behavior of regular solutions to a nematic liquid crystal system in Sobolev spaces $H^m(\R^3)$ for $m\geq 0$.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.