{
  "abstract": "We study axisymmetric self-similar solutions of the stationary Navier--Stokes equations with $(-3)$-homogeneous forces and no-slip boundary conditions in a half-space. For a fixed force without swirl, we characterize the interval of amplitudes for which solutions exist and describe the velocity singularity at its finite endpoints. For each parameter in this interval, a solution exists after adding a swirl force of any size, and it is unique among solutions with bounded profiles when the swirl force is sufficiently small. The proof uses the nonnegative contribution of swirl to a Riccati equation and a comparison estimate. We also prove that, when the tangential curl of the force is sufficiently small, there exists a unique solution with small velocity profiles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25432",
  "author_total": 3,
  "authors": [
    {
      "name": "Yun Wang"
    },
    {
      "name": "Chunjing Xie"
    },
    {
      "name": "Shaoheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5cr899temknwt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25432",
  "fulltext_url": null,
  "id": "5cr899temknwt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25432",
  "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": "W7204453733",
  "pdf_url": "https://arxiv.org/pdf/2608.25432",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5cr899temknwt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.25432",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25432"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Self-similar stationary Navier--Stokes flows in a half-space with arbitrarily large swirl forcing",
  "title_text": "Self-similar stationary Navier--Stokes flows in a half-space with arbitrarily large swirl forcing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5cr899temknwt",
  "venue": "arXiv",
  "versions": []
}