Global existence and optimal decay rate for the strong solutions in H2H2 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 H2H2. If further that the L1L1 norm of initial perturbation is finite, we prove the optimal L2L2 decay rates for such a solution and its first-order spatial derivatives.