Global Existence and Optimal Decay Rates for Three-Dimensional Compressible Viscoelastic Flows System with Damping

Abstract

In this paper, we consider the large time behavior of the strong solutions to the three dimensional compressible viscoelastic flows with damping. Based on the energy method and spectral analysis, we analyze the influences of the damping on the global existence and decay rates of compressible viscoelastic flows under some small assumptions in H 3-framework. Compared with the time decay rates of solutions to the compressible viscoelastic flows in [1], our results imply that the friction of the damping is stronger than the dissipation effect of the viscosities.