{
  "abstract": "The aim of this work is to extend the results from a recent paper by Hong, Li and Liu, from bounded domains to both bounded and unbounded domains. We show the global existence and uniqueness of 3D stochastic Navier-Stokes equations with nonlinear multiplicative noise for every initial data from the Sobolev space $H^1$. We do not use any tightness argument. Instead, we firstly show the existence of a local maximal solution and then we use Lyapunov function to prove the solution is global. Our approach is motivated by a recent paper of the first named author with Ferrario, Maurelli and Zanella about a similar result for stochastic nonlinear Schrödinger Equations. The main idea is that once the local existence of strong solutions is established, a very strong noise pushing toward the origin, will make blow-up impossible.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08284",
  "author_total": 3,
  "authors": [
    {
      "name": "Zdzisław Brzeźniak"
    },
    {
      "name": "Shijia Zhang"
    },
    {
      "name": "Guoli Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/be28xxjdpt1cj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08284",
  "fulltext_url": null,
  "id": "be28xxjdpt1cj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08284",
  "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.PR"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7212001078",
  "pdf_url": "https://arxiv.org/pdf/2609.08284",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/be28xxjdpt1cj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08284",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08284"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Global Existence and Stability of 3D Stochastic NSEs in Bounded and Unbounded Domains Driven by a Special Multiplicative Wiener Process",
  "title_text": "Global Existence and Stability of 3D Stochastic NSEs in Bounded and Unbounded Domains Driven by a Special Multiplicative Wiener Process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/be28xxjdpt1cj",
  "venue": "arXiv",
  "versions": []
}