{
  "abstract": "We study $(-1)$-homogeneous solutions of the steady Navier-Stokes equations in $\\mathbb R^n\\setminus\\{0\\}$ with $(-3)$-homogeneous, locally Lipschitz forces. Previous work [2] established the existence of $(-1)$-homogeneous solutions without any smallness assumption in dimensions $4\\leq n\\leq16$. In this paper, we remove the dimension restriction and obtain the existence of self-similar solutions in all higher dimensions. The new ingredient is a dimension-independent a priori estimate for the total head pressure on the sphere, obtained by adapting the source-flux method and the weighted identity of the pressure of Wang and Yang [28] to the homogeneous setting. This combines with the structural relation between the radial velocity and the total head pressure used in [2] to close the a priori estimates for the solutions in all dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09840",
  "author_total": 4,
  "authors": [
    {
      "name": "Changfeng Gui"
    },
    {
      "name": "Hao Liu"
    },
    {
      "name": "Yun Wang"
    },
    {
      "name": "Chunjing Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2frzf28bye9f5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09840",
  "fulltext_url": null,
  "id": "2frzf28bye9f5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09840",
  "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": "W7221031064",
  "pdf_url": "https://arxiv.org/pdf/2610.09840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2frzf28bye9f5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Self-similar solutions to the steady Navier-Stokes equations in arbitrarily high dimensions",
  "title_text": "Self-similar solutions to the steady Navier-Stokes equations in arbitrarily high dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/2frzf28bye9f5",
  "venue": "arXiv",
  "versions": []
}