Decay estimates for three-dimensional nematic liquid crystal system

Abstract

<abstract><p>In this paper, we consider the decay rates of the higher-order spatial derivatives of solution to the Cauchy problem of 3D compressible nematic liquid crystals system. The $ \dot{H}^s\; (\frac12 < s < \frac32) $ negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.</p></abstract>