Nonisothermal Richards flow in porous media with cross diffusion
Analysis of PDEs
2026-01-01 v3
Abstract
The existence of large-data weak entropy solutions to a nonisothermal immiscible compressible two-phase unsaturated flow model in porous media is proved. The model is thermodynamically consistent and includes temperature gradients and cross-diffusion effects. Due to the fact that some terms from the total energy balance are non-integrable in the classical weak sense, we consider so-called variational entropy solutions. A priori estimates are derived from the entropy balance and the total energy balance. The compactness is achieved by using the Div-Curl lemma.
Keywords
Cite
@article{arxiv.2102.00455,
title = {Nonisothermal Richards flow in porous media with cross diffusion},
author = {Esther S. Daus and Josipa Pina Milišić and Nicola Zamponi},
journal= {arXiv preprint arXiv:2102.00455},
year = {2026}
}