Continuity of the Saturation in the Flow of Two Immiscible Fluids in a Porous Medium

The weakly coupled system (1.3) below consists of an elliptic equation and a degenerate parabolic equation, and it arises in the theory of flow of immiscible fluids in a porous medium. The unknown functions u and v and the equations they satisfy, represent the pressure and the saturation respectively, subject to Darcy's law and the Buckley-Leverett coupling. Due to the empirical nature of these laws no determination is possible on the structure of the degeneracy exhibited by the system. It is established that the saturation is a locally continuous function in its space-time domain of definition, irrespective of the nature of the degeneracy of the principal part of the system.