Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows

In this paper, we are concerned with the global existence and optimal rates of strong solutions for three-dimensional compressible viscoelastic flows. We prove the global existence of the strong solutions by the standard energy method under the condition that the initial data are close to the constant equilibrium state in $H^2$-framework. If additionally the initial data belong to $L^1$, the optimal convergence rates of the solutions in $L^p$-norm with $2\le p\le 6$ and optimal convergence rates of their spatial derivatives in $L^2$-norm are obtained.