{
  "abstract": "This paper studies the 2D Navier--Stokes equation on a bounded domain with Navier-slip boundary conditions, driven by spatially localized stationary forcing generated by a stochastic heat equation. We prove exponential mixing for the associated Navier--Stokes--heat system, and consequently exponential convergence of the velocity law under stationary forcing. The main difficulty is that the white noise is confined to a subdomain and reaches the velocity indirectly through the heat component. To address the degeneracy, the proof combines Malliavin calculus with PDE control theory. The key ingredient is a stabilization scheme that converts localized Navier--Stokes controls into time-regular controls compatible with the heat dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28964",
  "author_total": 3,
  "authors": [
    {
      "name": "Ziyu Liu"
    },
    {
      "name": "Shengquan Xiang"
    },
    {
      "name": "Zhifei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ag3hj0dxps11q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28964",
  "fulltext_url": null,
  "id": "ag3hj0dxps11q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28964",
  "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.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7204938057",
  "pdf_url": "https://arxiv.org/pdf/2608.28964",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ag3hj0dxps11q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28964",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28964"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exponential mixing for the stochastic Navier--Stokes equation with localized noise",
  "title_text": "Exponential mixing for the stochastic Navier--Stokes equation with localized noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ag3hj0dxps11q",
  "venue": "arXiv",
  "versions": []
}