{
  "abstract": "For $n\\geq5$, let $(u,p)$ be a smooth solution of the stationary incompressible Navier-Stokes equations in $\\R^n\\setminus\\{x'=0\\}$, where $\\{x'=0\\}$ is the $x_n$-axis. We prove that the scale-invariant transverse bound $|u(x)|\\leq C |x'|^{-1}$ forces $u\\equiv0$. This result relies on a quantitative local regularity theorem, which shows that the transverse bound condition yields uniform control of $u$ and $\\nabla u$ in a smaller ball and removes the possible singularity along the axis. The proof combines weak extension across the axis, approximate Green functions for an adjoint drift operator, a one-sided bound for the total head pressure, a localized Frehse-Růžička weighted estimate, and a finite Stokes-Morrey bootstrap. Applying the local theorem at arbitrarily large scales yields whole-space rigidity and removability of line singularities. This together with the asymptotic expansions on the exterior domains in the case $|u(x)|\\leq C |x|^{-1}$ in [1], yields the same expansion in exterior domains under the condition $|u(x)|\\leq C |x'|^{-1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26323",
  "author_total": 4,
  "authors": [
    {
      "name": "Changfeng Gui"
    },
    {
      "name": "Hao Liu"
    },
    {
      "name": "Yun Wang"
    },
    {
      "name": "Chunjing Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/000cz0wnq4nh7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26323",
  "fulltext_url": null,
  "id": "000cz0wnq4nh7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26323",
  "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": "W7214087722",
  "pdf_url": "https://arxiv.org/pdf/2609.26323",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/000cz0wnq4nh7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26323",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26323"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Rigidity of Stationary Navier-Stokes Solutions with Transverse bound in Dimensions Five and Higher",
  "title_text": "Rigidity of Stationary Navier-Stokes Solutions with Transverse bound in Dimensions Five and Higher",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/000cz0wnq4nh7",
  "venue": "arXiv",
  "versions": []
}