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arXiv · 2601.01374

On the well-posedness of two-dimensional Muskat problem with an elastic interface

Lizhe Wan·Jiaqi Yang
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Abstract

We investigate the two-dimensional Muskat problem with a nonlinear elastic interface, for both one-phase and two-phase scenarios. Following the framework developed by Nguyen [35,36], we demonstrate that the problem is locally well-posed in $H^s$ for $s\geq 2$ for arbitrary initial data. Furthermore, for the one-phase case and the stable two-phase case $(\rho^+ \leq \rho^-)$, we establish global well-posedness for small initial data in $H^s$ when $s> \frac{3}{2}$.

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Lizhe Wan, Jiaqi Yang. 2026-01-04. On the well-posedness of two-dimensional Muskat problem with an elastic interface. https://arxiv.org/abs/2601.01374

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