Existence result for stationary compressible fluids and asymptotic behavior in thin films

Abstract

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