On a fully coupled nonlinear parabolic problem modelling miscible compressible displacement in porous media

We study a model describing a compressible and miscible displacement in a porous medium. It consists of a coupled system of nonlinear parabolic partial differential equations. Using nonclassical estimates and renormalization tools, we prove the existence of relevant weak solutions for the problem. This is the first existence result obtained for a transport model containing both the coupling due to the compressibility assumption and the coupling due to the concentration dependent viscosity.