Decay of the compressible viscoelastic flows

Abstract

In this paper we study the time decay rates of the solution to the Cauchy problem for the compressible viscoelastic flows via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, and the $\dot{H}^{-s}(0\leq s<\frac{3}{2})$ negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.