Open Access
Translator Disclaimer
2017 Incompressible immiscible multiphase flows in porous media: a variational approach
Clément Cancès, Thomas O. Gallouët, Léonard Monsaingeon
Anal. PDE 10(8): 1845-1876 (2017). DOI: 10.2140/apde.2017.10.1845


We describe the competitive motion of N+1 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, N 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.


Download Citation

Clément Cancès. Thomas O. Gallouët. Léonard Monsaingeon. "Incompressible immiscible multiphase flows in porous media: a variational approach." Anal. PDE 10 (8) 1845 - 1876, 2017.


Received: 13 July 2016; Revised: 23 May 2017; Accepted: 29 June 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1370.35230
MathSciNet: MR3694008
Digital Object Identifier: 10.2140/apde.2017.10.1845

Primary: 35A15 , 35K65 , 49K20 , 76S05

Keywords: constrained parabolic system , minimizing movement scheme , multiphase porous media flows , Wasserstein gradient flows

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.10 • No. 8 • 2017
Back to Top