Global existence and optimal decay rate for the strong solutions in to the compressible Navier–Stokes equations

We prove the global existence of a unique strong solution to the compressible Navier–Stokes equations when the initial perturbation is small in H 2 . If further that the L 1 norm of initial perturbation is finite, we prove the optimal L 2 decay rates for such a solution and its first-order spatial derivatives.