A fluid-solid interaction problem in porous media
Analysis of PDEs
2026-02-12 v1 Fluid Dynamics
Abstract
In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution equations that capture the free-boundary dynamics up to quadratic order. In the long-wave thin-film regime, we rewrite the kinematic condition in flux form, flatten the moving domain, and derive a lubrication-type equation. Moreover, we establish well-posedness for these models in suitable Wiener spaces.
Cite
@article{arxiv.2602.10822,
title = {A fluid-solid interaction problem in porous media},
author = {Diego Alonso-Orán and Rafael Granero-Belinchón},
journal= {arXiv preprint arXiv:2602.10822},
year = {2026}
}