Global existence for a two-phase flow model with cross diffusion
Analysis of PDEs
2019-05-27 v2
Abstract
In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent relaxation parameter and hypocoercive diffusion operator modeling cross diffusion. The equations are derived in a thermodynamically correct way from mass conservation laws. Global-in-time existence of weak solutions to the system in a bounded domain with equilibrium boundary conditions is shown. The main tools of the analysis are an entropy inequality and a crucial apriori bound which allows for controlling the degeneracy.
Cite
@article{arxiv.1901.07296,
title = {Global existence for a two-phase flow model with cross diffusion},
author = {Esther S. Daus and Josipa-Pina Milišić and Nicola Zamponi},
journal= {arXiv preprint arXiv:1901.07296},
year = {2019}
}