{
  "abstract": "We study the three-dimensional incompressible Navier--Stokes equations on the torus with multiplicative Itô noise which is driven by a single Brownian motion and acts only through the vertical velocity component. Such a noise is strongly degenerate: An infinite-dimensional part of the velocity field is not forced at all. We show that it nevertheless has a regularizing effect. For a linear noise, strong solutions whose initial data have no unforced part are global with probability tending to one as the noise intensity grows. For a suitable nonlinear noise, the same holds for arbitrary $\\mathrm{H}^1$ data, together with smallness of the space-time $\\mathrm{L}^6$-norm of the vertical velocity. As a deterministic counterpart, we give a self-contained proof that a quintic damping of the vertical component yields global regularity, and the same argument shows that, under the linear noise, blow-up can only occur if the vertical velocity leaves $\\mathrm{L}^6_{t,x}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02557",
  "author_total": 2,
  "authors": [
    {
      "name": "Felix Brandt"
    },
    {
      "name": "Igor Kukavica"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fe1d0bvpjqrs0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02557",
  "fulltext_url": null,
  "id": "fe1d0bvpjqrs0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02557",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fe1d0bvpjqrs0.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02557"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Regularizing the Navier-Stokes Equations by One Noise Component",
  "title_text": "Regularizing the Navier-Stokes Equations by One Noise Component",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/fe1d0bvpjqrs0",
  "venue": "arXiv",
  "versions": []
}