{
  "abstract": "Let $(v,p)$ be a smooth stationary Navier--Stokes solution in $\\mathbb R^3$ with $v(x)\\to0$ as $|x|\\to\\infty$. We prove that $v\\equiv0$ if its vorticity $ω:=\\nabla \\times v$ belongs to $L^{s,\\infty}(\\mathbb R^3)$ for some $9/5\\le s\\le1.87$. This gives a global weak-Lorentz vorticity criterion beyond $9/5$ requiring neither smallness nor an additional Fubini-type hypothesis. The finite Dirichlet integral is recovered from the vorticity hypothesis rather than assumed. In particular, $|ω(x)|=O(|x|^{-α})$ implies triviality for $α\\ge300/187$, crossing the $|x|^{-5/3}$ vorticity-decay scale. The proof combines this automatic finite-energy upgrade with a new variable-denominator Bernoulli--vorticity quotient identity. Its completed-square form gives nonnegative defect terms, and localizing the concavity of the denominator creates a positive measure on a Bernoulli level surface. A pressure-weighted convex extension of this identity yields a quantitative normalized-vorticity trace and quotient-gradient control. These estimates are then coupled to the Bernoulli-gradient identity through a nonlinear feedback estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22471",
  "author_total": 1,
  "authors": [
    {
      "name": "Wangzhe Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2g9yfv304zch0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22471",
  "fulltext_url": null,
  "id": "2g9yfv304zch0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22471",
  "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": "W7204158803",
  "pdf_url": "https://arxiv.org/pdf/2608.22471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2g9yfv304zch0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.22471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Beyond the $L^{9/5}$ Vorticity Criterion in the Stationary Navier--Stokes Liouville Problem",
  "title_text": "Beyond the L^9/5 Vorticity Criterion in the Stationary Navier--Stokes Liouville Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/2g9yfv304zch0",
  "venue": "arXiv",
  "versions": []
}