Asymptotic Behavior of Solutions to the Liquid Crystal System in   $H^m(\mathbb{R}^3)$
  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. 
Mimi Dai and Maria E. Schonbek
math.AP