Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 122, pp. 1-33.

Title: Solutions to a model for compressible immiscible two phase flow
       in porous media

Author: Ziad Khalil (Ecole Centrale de Nantes, France)
        Mazen Saad  (Ecole Centrale de Nantes, France)

Abstract:
 In this article, we study the existence of solutions to
 a nonlinear degenerate system modelling the displacement
 of two-phase compressible immiscible flow  in a three
 dimensional  porous media. The aim of this work is to
 treat the model with its general form with the whole
 nonlinear terms. Especially, we consider the case where
 the density of each phase depends on its corresponding pressure.
 We derive new energy estimates on velocities, saturations and
 pressures to treat the degeneracy of the system.
 A compactness result is shown for degenerate systems.
 
Submitted May 7, 2010. Published August 30, 2010.
Math Subject Classifications: 35K57, 35K55, 92D30.
Key Words: Degenerate system; nonlinear parabolic system;
           compressible flow; porous media.