{
  "abstract": "We study two physically distinct steady free-boundary problems in a two-dimensional inviscid fluid: a hollow vortex in a constant-vorticity flow subject to simple shear, third order and linear strain at infinity, without surface tension, and an irrotational flow past a constant-pressure bubble subject to surface tension, linear strain, and circulation at infinity. Building on the mathematical vortex-bubble correspondence recently developed by Crowdy and Tanveer, we show that both problems are linked by a common mathematical formulation. For the vortex problem, we extend the sequence-space fixed-point approach of Crowdy and Tanveer to obtain new local existence, uniqueness, and analyticity results. For the bubble problem, we develop a separate existence theory, reducing it to a nonlinear singular integral operator fixed-point problem and deriving a scalar solvability condition that defines a realanalytic surface in the physical parameter space. On this surface we obtain locally unique bubble solutions with real-analytic boundaries and holomorphically extendible velocity fields. Finally, we prove that the scalar solvability condition is equivalent to a functional conformal mapping identity. The scalar condition between the parameters is enough for the vortex and bubble problems to have the same free-boundary shape, despite their different exterior flows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07709",
  "author_total": 3,
  "authors": [
    {
      "name": "Valentin D. Kunz"
    },
    {
      "name": "Saleh Tanveer"
    },
    {
      "name": "Darren G. Crowdy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aay6m87vsja4g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07709",
  "fulltext_url": null,
  "id": "aay6m87vsja4g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07709",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7220932919",
  "pdf_url": "https://arxiv.org/pdf/2610.07709",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aay6m87vsja4g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.07709",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07709"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A mathematical analogy between certain hollow vortex and bubble flows - existence, uniqueness, and identical boundary shapes",
  "title_text": "A mathematical analogy between certain hollow vortex and bubble flows - existence, uniqueness, and identical boundary shapes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/aay6m87vsja4g",
  "venue": "arXiv",
  "versions": []
}