degenerate two-phase compressible immiscible flow in porous media: the case where the density of each phase depends on its own pressure

in this paper, we consider a model of flow of two compressible and immiscible phases in a three-dimensional porous media. the equations are obtained by the conservation of the mass of each phase. this model is treated in its general form with the whole nonlinear terms. we establish an existence result for this model based on new energy estimates to handle the dependence of densities on the corresponding pressure of each phase.