{
  "abstract": "We establish upper bounds for vorticity and related quantities in axisymmetric Euler flows without swirl in $\\mathbb{R}^3$, assuming that the initial relative vorticity $ω_0/r$ belongs to $L^1\\cap L^p$ with $3<p\\le \\infty$. For each fixed $p \\in (3,\\infty]$, we obtain polynomial-in-time upper bounds for the radial moments, the radial velocity, and the $L^p$ norm of vorticity. We then consider initial data with unbounded relative vorticity whose growth near the axis is controlled by $Φ(\\log \\tfrac{1}{r})$ for a subexponential profile $Φ$, so that $ω_0/r$ belongs to $L^p$ for every $p<\\infty$ but not to $L^{\\infty}$. For such data, we derive profile dependent upper bounds for the vorticity maximum. In particular, for any polynomial function $Φ(s)=s^k$ with $k\\ge 0$, we show that $\\|ω(\\cdot,t)\\|_{L^{\\infty}}$ is bounded by $(1+t)^{\\frac{4}{3}+k} (\\log (2+t) )^{\\frac{2k}{3}}$. Moreover, for initial data satisfying $ω_0/r \\in L^1\\cap L^p$ with a fixed $p\\in (3,\\infty)$, under additional symmetry and vertical confinement assumptions, we obtain a subexponential-in-time upper bound for the vorticity maximum, thereby improving the classical exponential bound for such data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26559",
  "author_total": 1,
  "authors": [
    {
      "name": "Khakim Egamberganov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bkjtdyh7qcnjg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26559",
  "fulltext_url": null,
  "id": "bkjtdyh7qcnjg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26559",
  "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": "W7223047481",
  "pdf_url": "https://arxiv.org/pdf/2610.26559",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bkjtdyh7qcnjg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26559",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26559"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Vorticity growth beyond bounded relative vorticity for axisymmetric Euler flows without swirl",
  "title_text": "Vorticity growth beyond bounded relative vorticity for axisymmetric Euler flows without swirl",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/bkjtdyh7qcnjg",
  "venue": "arXiv",
  "versions": []
}