Global existence and optimal decay rate for the strong solutions in to the 3-D compressible Navier–Stokes equations without heat conductivity

In this paper, we consider the 3-D compressible Navier–Stokes equations without heat conductivity, which form a hyperbolic–parabolic system. We prove the global existence of a strong solution when the initial perturbation is small in H 2 and its L 1 -norm is bounded. Moreover, we can obtain the optimal decay rates for such a solution.