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In this paper, we are concerned with the global existence and optimal ratesof strong solutions for three-dimensional compressible viscoelastic flows. Weprove the global existence of the strong solutions by the standard energymethod under the condition that the initial data are close to the constantequilibrium state in $H^2$-framework. If additionally the initial data belongto $L^1$, the optimal convergence rates of the solutions in $L^p$-norm with$2\leq p\leq 6$ and optimal convergence rates of their spatial derivatives in$L^2$-norm are obtained.

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