Globally bounded trajectories for the barotropic Navier-Stokes system with general boundary conditions

We consider the barotropic Navier–Stokes system describing the motion of a viscous compressible fluid interacting with the outer world through general in/out flux boundary conditions. We consider a hard–sphere type pressure EOS and show that all trajectories eventually enter a bounded absorbing set. In particular, the associated omega-limit sets are compact and support a stationary statistical solution.