On existence and uniqueness results for a coupled systems modeling miscible displacement in porous media (Q1910856)

A model for the motion of two miscible fluids in a porous medium, both incompressible, one displaced by the other, is built by a nonlinear system of two equations: the one for the pressure is elliptic, while the other, which corresponds to one of the fluids concentration, is parabolic. This paper considers the model in two space dimensions to reach uniqueness of the so-called semiclassical solutions, and existence of a weak solution, this latter result is obtained by the regularization technique. Most of the results are claimed to be independent of the space dimension.