{
  "abstract": "In this paper, we consider the existence and stability of waves progressing through a finite-depth two-dimensional body of water that carry a vortex in their bulk. The waves are acted upon by gravity, and sit below a region of air at constant pressure, with the air--water interface being a free boundary along which capillary effects are incorporated. We consider two classes of vortices: point vortices, where formally the vorticity is a Dirac $δ$, and hollow vortices, where the vortex core is a region of constant pressure outside the fluid domain and about which there is a nonzero circulation. First, we prove that steady small-amplitude wave-borne point vortices exist for any subcritical Froude number and supercritical Bond number, and then show they are conditionally orbitally stable. Second, through a vortex desingularization argument, we construct capillary-gravity wave-borne hollow vortices. Notably, the wave speed is $O(1)$ for both these families.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29791",
  "author_total": 3,
  "authors": [
    {
      "name": "Gregory Slease"
    },
    {
      "name": "Samuel Walsh"
    },
    {
      "name": "Runzhang Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/df3zjqc829atd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29791",
  "fulltext_url": null,
  "id": "df3zjqc829atd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29791",
  "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",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7214366590",
  "pdf_url": "https://arxiv.org/pdf/2609.29791",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/df3zjqc829atd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29791",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29791"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Existence and stability of capillary-gravity wave-borne vortices",
  "title_text": "Existence and stability of capillary-gravity wave-borne vortices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/df3zjqc829atd",
  "venue": "arXiv",
  "versions": []
}