Time decay rates for the compressible viscoelastic flows

In this paper, we investigate the time decay rates of the global smooth solutions to the compressible viscoelastic flows in R3. The global existence and uniqueness of smooth solutions are obtained under the assumption that the H3 norm of the initial data is small, but the higher order derivatives can be arbitrarily large. Moreover, if the initial data is bounded in H˙−s(0≤s<32) or B˙2,∞−s(0