Existence result for degenerate cross-diffusion system with application to seawater intrusion

In this paper, we study degenerate parabolic system, which are strongly coupled. We prove general existence result, but the uniqueness remains an open question. Our proof of existence is based on a crucial entropy estimate which both control the gradient of the solution and the non-negativity of the solution. Our system are of porous medium type and our method applies to models in seawater intrusion.