{
  "abstract": "In this note, we revisit a Liouville-type theorem of Chae and Wolf for stationary Navier-Stokes equations in $\\mathbb{R}^3$ [J. Differential Equations 261 (2016) 5541-5560]. We show that their logarithmic improvement of the classical $L^{9/2}$ condition is part of a substantially broader weighted framework. More precisely, we prove that a solution $u\\in\\dot H^1(\\mathbb{R}^3)$ is necessarily trivial whenever $$ \\int_{\\mathbb{R}^3}|u(x)|^{9/2}\\,ω(|u(x)|)\\,dx< +\\infty, $$ for every positive, nondecreasing and bounded weight $ω$ satisfying a mild growth condition near the origin. This structural condition encompasses the logarithmic weight due to Chae and Wolf, as well as a hierarchy of iterated-logarithmic weights and (genuinely) non-logarithmic examples, including a dyadic weight. Our result identifies a broader class of weighted integrability conditions under which the triviality of stationary Navier-Stokes solutions follows, and shows that the mechanism underlying the Chae-Wolf improvement is not intrinsically tied to a specific logarithmic weight or to a single logarithmic scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06013",
  "author_total": 2,
  "authors": [
    {
      "name": "Raúl Fierro"
    },
    {
      "name": "Gaston Vergara-Hermosilla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6p68ah0ghkx8f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06013",
  "fulltext_url": null,
  "id": "6p68ah0ghkx8f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06013",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7212074733",
  "pdf_url": "https://arxiv.org/pdf/2609.06013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6p68ah0ghkx8f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Remarks on a Liouville-type theorem by Chae and Wolf for stationary Navier-Stokes equations",
  "title_text": "Remarks on a Liouville-type theorem by Chae and Wolf for stationary Navier-Stokes equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6p68ah0ghkx8f",
  "venue": "arXiv",
  "versions": []
}