Stabilization to equilibria of compressible Navier–Stokes equations with infinite mass

We consider the compressible Navier–Stokes equations in an exterior three-dimensional domain with non-zero constant density prescribed at infinity. We assume that p(ϱ)=ϱγp(ϱ)=ϱγ, γ>32, and that the force is potential. We show that for time tending to infinity, the density approaches the unique solution to the stationary problem, provided the potential satisfies certain regularity and structural assumptions.