{
  "abstract": "We consider the Navier-Stokes equations in a smooth bounded domain $D\\subset \\mathbb R^3$. It has been proved in arXiv:2609.08284 that these equations have a unique solution - globally defined in time - when a superlinear noise is introduced and the initial velocity belongs to the space $V$ of divergence-free $H^1_0(D;\\mathbb R^3)$-vector fields. Here we show that the same result holds when there is also an additive noise and a deterministic forcing term. Moreover, when the deterministic forcing term is time-independent we prove the existence of at least one invariant measure for this stochastic equation. This is obtained by the Krylov-Bogoliubov method, based on tightness and Feller property in $V$. Finally, we show that the set of invariant measures contains one ergodic invariant measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13266",
  "author_total": 3,
  "authors": [
    {
      "name": "Zdzislaw Brzezniak"
    },
    {
      "name": "Benedetta Ferrario"
    },
    {
      "name": "Margherita Zanella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2da8xc5yze6mk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13266",
  "fulltext_url": null,
  "id": "2da8xc5yze6mk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13266",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7221529087",
  "pdf_url": "https://arxiv.org/pdf/2610.13266",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2da8xc5yze6mk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13266",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13266"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Existence of ergodic invariant measures for 3D Navier-Stokes eqs with superlinear noise",
  "title_text": "Existence of ergodic invariant measures for 3D Navier-Stokes eqs with superlinear noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/2da8xc5yze6mk",
  "venue": "arXiv",
  "versions": []
}