A note on variable-density flows in porous media (Q6595452)

The motion of a fluid and solute transport through a rigid porous medium gets importance in the mathematical and computer modelling for polluted water in underground deposits and mines, for petroleum reservoir flows, among others. The article deals with a fully nonlinear degenerate strongly coupled parabolic system describing variable-density flows of a two-component mixture through porous media.\N\NThe author observes that no proof of well-posedness is known so far at this context. Neverthless, under physically reasonable hypotheses on the data, the exponential constitutive equation and the mixed boundary conditions, he reaches a global-in-time existence of weak solutions to the associated initial-boundary value problem, assuming that the volumetric solutal expansion coefficient is sufficiently small.