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PreprintarXiv licencearXiv

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 𝕊2 with multilinear singular integral estimates that exploit a crucial null structure in the nonlinear terms.

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Cite

BibTeXRIS
BibTeX
@misc{gancedo2026nonlinear,
  title = {{Nonlinear Stability of 3D Muskat Bubbles}},
  author = {Francisco Gancedo and Eduardo García-Juárez and Susanna V. Haziot and Neel Patel and Robert M. Strain},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30197},
  eprint = {2609.30197},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30197},
}
RIS
TY  - UNPB
TI  - Nonlinear Stability of 3D Muskat Bubbles
AU  - Francisco Gancedo
AU  - Eduardo García-Juárez
AU  - Susanna V. Haziot
AU  - Neel Patel
AU  - Robert M. Strain
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30197
UR  - https://arxiv.org/abs/2609.30197
AB  - 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 𝕊^2 with multilinear singular integral estimates that exploit a crucial null structure in the nonlinear terms.
ER  -