The optimal convergence rates for the multi-dimensional compressible viscoelastic flows

In this paper, we are concerned with the multi-dimensional (N≥3) compressible viscoelastic flows in the whole space. We prove the optimal convergence rates of strong solutions to the system for the initial data close to a stable equilibrium state in critical Besov spaces. Our main ideas are based on the low-high frequency decomposition and the smooth effect of dissipative operator.