An Existence Result for Multidimensional Immiscible Two-Phase Flows with Discontinuous Capillary Pressure Field

We consider the system of equations governing an incompressible immiscible two-phase flow within an heterogeneous porous medium made of two different rock types. Since the capillary pressure function depends on the rock type, the capillary pressure field might be discontinuous at the interface between the rocks. We introduce multivalued phase pressures to give a sense to the transmission conditions at the interface. We prove the existence of a solution for such a flow by passing to the limit in regularizations of the problem. keywords: two-phase flows, porous media, discontinuous capillarity, multivalued pressures AMS subject classification: 35M33, 35Q86, 35K65, 76S05, 76T99