Karam Allali, Vitaly Volpert and Vitali Vougalter
On a Model of Miscible Liquids in Porous Media
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ABSTRACT.  In this paper we study interaction of two miscible liquids in porous media. The model consists of a system of coupled hydrodynamic equations 
with Korteweg stress terms and 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 forces functions. Numerical simulations are performed to show the behavior of two miscible liquids subjected to Korteweg stress.