We describe the competitive motion of
incompressible immiscible phases within a porous medium as the gradient flow
of a singular energy in the space of nonnegative measures with prescribed
masses, endowed with some tensorial Wasserstein distance. We show the
convergence of the approximation obtained by a minimization scheme á
la R. Jordan, D. Kinderlehrer and F. Otto (SIAM J. Math. Anal.29:1
(1998) 1–17). This allows us to obtain a new existence result for a physically
well-established system of PDEs consisting of the Darcy–Muskat law for each phase,
capillary pressure relations, and a constraint on the volume occupied by the fluid.
Our study does not require the introduction of any global or complementary
pressure.
We have not been able to recognize your IP address
34.239.150.57
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.