Rémy Sart

Existence of finite energy weak solutions for the equations MHD of compressible fluids

This article concerns the existence of global weak solutions for a compressible Magnetohydrodynamic model. We assume the viscosity and the resistivity to be constant and we prove that Feireisl and Lionss strategies dedicated to the usual barotropic compressible flows may be extended to our system. The only difficulty to be taken into account is the magnetic field dependency. The case with density-dependent viscosity and resistivity coefficients will be treated in a forthcoming paper following Bresch and Desjardinss strategy.

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.