Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media

Abstract

In this paper we study the existence and partial regularity of weak solutions to an elliptic-parabolic system that models the single-phase miscible displacement of one incompressible fluid by another in a porous medium. The system is singular and involves quadratic nonlinearity. The partial regularity result is obtained via the Fefferman-Stein inequality.