{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30197",
  "author_total": 5,
  "authors": [
    {
      "name": "Francisco Gancedo"
    },
    {
      "name": "Eduardo García-Juárez"
    },
    {
      "name": "Susanna V. Haziot"
    },
    {
      "name": "Neel Patel"
    },
    {
      "name": "Robert M. Strain"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d49c0a7fe91ap.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30197",
  "fulltext_url": null,
  "id": "d49c0a7fe91ap",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30197",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214369533",
  "pdf_url": "https://arxiv.org/pdf/2609.30197",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d49c0a7fe91ap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30197",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30197"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nonlinear Stability of 3D Muskat Bubbles",
  "title_text": "Nonlinear Stability of 3D Muskat Bubbles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/d49c0a7fe91ap",
  "venue": "arXiv",
  "versions": []
}