On a degenerate parabolic system for compressible, immiscible, two-phase flows in porous media

Abstract

The aim of this paper is to analyze a model of a degenerate nonlinear system arising from immiscible, compressible, two-phase, three-dimensional flows occurring in porous media. A degenerate weighted formulation is introduced to take into account the compressibility and the degeneracy. Two existence results of such a degenerate weak solution are introduced. The first result concerns the existence of solutions under a reasonable assumption on the capillary pressure. This condition allows the degeneracy only where one of the two phases is exclusively present. The second result establishes, for suitable initial data, the existence of solutions when the degeneracy occurs where one or the other phase is exclusively present. Nevertheless, for suitable initial data, a classical weak solution is obtained when the degeneracy is not too strong and occurs only where the injected phase is exclusively present.