Compressible flows: New existence results and justification of the Reynolds asymptotic in thin films

In this paper, we are first interested in the compressible Navier-Stokes equations with density dependent viscosities in bounded domains with non-homogeneous Dirichlet conditions. We study the well posedness of such models with density dependent viscosity coefficients in the non-stationary and in the stationary cases. We apply the last result in thin domains context, justifying the compressible Reynolds equations.