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arXiv · 2604.06545

Global well-posedness of the one-phase Muskat problem with surface tension

Hongjie Dong·Hyunwoo Kwon
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Abstract

In this paper, we establish the global well-posedness of the one-phase Muskat problem with surface tension for small initial data. This problem describes the motion of the interface separating a wet region from a dry region within a porous medium, a process governed by Darcy's law. Although physically essential, the inclusion of surface tension introduces an additional challenge. We prove that if the initial free boundary is sufficiently small in $H^s$, $s>d/2+1$, then the problem admits a unique global strong solution. Moreover, the solution converges to zero in Lipschitz norm as $t\rightarrow\infty$. To the best of our knowledge, this work constitutes the first global well-posedness result for the one-phase Muskat problem with surface tension.

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Hongjie Dong, Hyunwoo Kwon. 2026-04-08. Global well-posedness of the one-phase Muskat problem with surface tension. https://arxiv.org/abs/2604.06545

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