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

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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.