MATHEMATICAL-ANALYSIS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT MODELS IN POROUS-MEDIA

We discuss a three-dimensional displacement model of one miscible comp ressible fluid by another in a porous medium. The motion is modeled by a nonlinear system of parabolic type coupling the pressure and the co ncentration. We give an existence result of weak solutions for a model with diffusion and dispersion, using the Schauder fixed point theorem . We also study a model in the absence of diffusion and dispersion. Th e system becomes of parabolic-hyperbolic type, the existence of global weak solutions is then obtained through a compensated compactness arg ument.