{
  "abstract": "We study the axisymmetric incompressible Euler equations in $\\mathbb{R}^3$ with a small initial swirl. Fix $s>7/2$, and let $\\boldsymbol{v}_0\\in H^s(\\mathbb{R}^3)$ be axisymmetric and divergence-free. If $\\varepsilon=\\|{\\nabla\\times(v_{0,θ}\\boldsymbol{e}_θ)}\\|_{L^\\infty}$ is sufficiently small, then the lifespan $T_*$ of the corresponding $H^s$ solution satisfies $$ T_{*}\\geq\\frac{C_s}{1+\\|{\\boldsymbol{v}_0}\\|_{H^s}} \\left[ \\log\\log (\\varepsilon^{-1}) \\right]^{3/7}\\,. $$ This removes the assumption by Danchin (Proc. Amer. Math. Soc. 141:1979-1993, 2013) that the domain must be distant from the axis of symmetry. Moreover, even for $\\boldsymbol{v}_0\\in H^3$, our result improves the fourfold iterated-logarithmic lower bound for the lifespan obtained by Li and Zhou (Z. Angew. Math. Phys. 75:219, 2024) to a threefold iterated-logarithmic bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25888",
  "author_total": 3,
  "authors": [
    {
      "name": "Zijin Li"
    },
    {
      "name": "Xu Xiao"
    },
    {
      "name": "Linbin Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6n2tky2h5k452.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25888",
  "fulltext_url": null,
  "id": "6n2tky2h5k452",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25888",
  "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": "W7223006511",
  "pdf_url": "https://arxiv.org/pdf/2610.25888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6n2tky2h5k452.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.25888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A double-logarithmic lifespan bound for axisymmetric Euler equations with a small initial swirl",
  "title_text": "A double-logarithmic lifespan bound for axisymmetric Euler equations with a small initial swirl",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/6n2tky2h5k452",
  "venue": "arXiv",
  "versions": []
}