Asymptotic Behavior of the stokes approximation equations for compressible flows in R3

We consider the Stokes approximation equations for compressible flows in R3. The global unique solution and optimal convergence rates are obtained by pure energy method provided the initial perturbation around a constant state is small. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. As an immediate byproduct, the usual Lp−L2(1≤p≤2) type of the optimal decay rate follow without requiring that the LP norm of initial data is small.