Global existence and asymptotic behavior for the 3D compressible Navier–Stokes equations without heat conductivity in a bounded domain

Abstract

In this paper, we investigate the global existence and uniqueness of strong solutions to the initial boundary value problem for the 3D compressible Navier–Stokes equations without heat conductivity in a bounded domain with slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in H2(Ω). Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.