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arXiv · 2609.30197

Nonlinear Stability of 3D Muskat Bubbles

Francisco Gancedo·Eduardo García-Juárez·Susanna V. Haziot·Neel Patel·Robert M. Strain
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Abstract

This paper studies the three-dimensional Muskat problem for two immiscible fluids in a porous medium subject to gravity and surface tension. We consider the setting in which one fluid forms a bounded bubble surrounded by the other. For any value of the physical parameters, we prove the global-in-time nonlinear asymptotic stability of a translating spherical bubble for small initial perturbations in the critical Lipschitz class. This enlarges the class of critical spaces considered in previous two-dimensional bubble results. The proof combines spectral analysis of the linearized operator on $\mathbb{S}^2$ with multilinear singular integral estimates that exploit a crucial null structure in the nonlinear terms.

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Francisco Gancedo, Eduardo García-Juárez, Susanna V. Haziot, Neel Patel, Robert M. Strain. 2026-09-24. Nonlinear Stability of 3D Muskat Bubbles. https://arxiv.org/abs/2609.30197

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