Navier-stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case

We consider the equations which describe the motion of a viscous compressible fluid, taking into consideration the case of inflow and/or outflow through the boundary. By means of some a priori estimates we prove the existence of a global (in time) solution. Moreover, as a consequence of a stability result, we show that there exist a periodic solution and a stationary solution.