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Mathematical analysis for compressible miscible displacement models in porous media. (English) Zbl 0859.35087

Authors’ summary: “We discuss a three-dimensional displacement model of one miscible compressible fluid by another in a porous medium. The motion is modeled by a nonlinear system of parabolic type coupling the pressure and the concentration. 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. The system becomes of parabolic-hyperbolic type, the existence of global weak solutions is then obtained through a compensated compactness argument”.
Reviewer: M.Biroli (Monza)

MSC:

35Q30 Navier-Stokes equations
35D05 Existence of generalized solutions of PDE (MSC2000)
76S05 Flows in porous media; filtration; seepage
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