{
  "abstract": "We study Liouville-type results for the stationary Navier--Stokes equations in $\\mathbb{R}^3$. We prove that any $\\dot{H}^1(\\mathbb{R}^3)$ solution is trivial under an integrability condition imposed only on the radial component of the velocity, namely $u_ρ(x) \\in L^p(\\mathbb{R}^3)$ with $3/2 < p \\leq 3$. We also establish a uniqueness result in a variable-exponent setting, where an $L^6$-type condition is required only on a bounded region, while the exponent approaches the critical value $3$ at infinity. Our analysis reveals that the rigidity of the stationary Navier--Stokes system can be driven by localized and radial integrability properties, rather than uniform global conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.05647",
  "author_total": 1,
  "authors": [
    {
      "name": "Gaston Vergara-Hermosilla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97een9tk6pvg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.05647",
  "fulltext_url": null,
  "id": "97een9tk6pvg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.05647",
  "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": "W7160667862",
  "pdf_url": "https://arxiv.org/pdf/2605.05647",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/97een9tk6pvg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2605.05647",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.05647"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component",
  "title_text": "Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/97een9tk6pvg1",
  "venue": "arXiv",
  "versions": []
}