Electron. J. Diff. Equ., Vol. 2015 (2015), No. 264, pp. 1-10.

A model of miscible liquids in porous media

Karam Allali, Vitaly Volpert, Vitali Vougalter

In this article we study the interaction of two miscible liquids in porous media. The model consists of hydrodynamic equations with the Korteweg stress terms coupled with the reaction-diffusion equation for the concentration. We assume that the fluid is incompressible and its motion is described by the Darcy law. The global existence and uniqueness of solutions is established for some optimal conditions on the reaction source term and external force functions. Numerical simulations are performed to show the behavior of two miscible liquids subjected to the Korteweg stress.

Submitted June 3, 2015. Published October 12, 2015.
Math Subject Classifications: 35A01, 35A02, 76D03, 76S05.
Key Words: Darcy approximation; Korteweg stress; miscible liquids; porous media.

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Karam Allali
Department of Mathematics
Faculty of Sciences and Technologies
University Hassan II
PO Box 146, Mohammedia, Morocco
email: allali@fstm.ac.ma
Vitaly Volpert
Institute Camille Jordan
University Lyon 1, UMR 5208 CNRS
69622 Villeurbanne, France
email: volpert@math.univ-lyon1.fr
Vitali Vougalter
University of Toronto
Department of Mathematics
Toronto, ON, M5S 2E4, Canada
email: vitali@math.toronto.edu

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