In this article, we study the existence and uniqueness of solutions for miscible liquids model in porous media. The model describing the phenomenon is a system of equations coupling hydrodynamic equations with concentration equation taking into account the Korteweg stress. We assume that the fluid is incompressible and its motion is described by the Darcy law. We prove the existence and uniqueness of global solutions for the initial boundary value problem.
Submitted September 30, 2013. Published November 20, 2013.
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
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