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arXiv · 1901.07296

Global existence for a two-phase flow model with cross diffusion

Esther S. Daus·Josipa-Pina Milišić·Nicola Zamponi
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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.

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Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi. 2019-01-22. Global existence for a two-phase flow model with cross diffusion. https://arxiv.org/abs/1901.07296

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