On a fully coupled nonlinear parabolic problem modelling miscible compressible displacement in porous media (Q2465870)

The author studies the well-posedness for an initial boundary value problem for a multidimensional coupled nonlinear system of parabolic equations which describes a compressible and miscible displacement in a porous medium and contains the three main mechanisms coupling the pressure with the concentration, that is the dispersive effects, the compressibility and the concentration-dependent viscosity. The main difficulty of the problem is its very strong coupling. Using non-classical estimates and renormalization tools (to get an estimate for the space derivatives of the Darcy velocity), the author proves the global existence of weak solutions.