{
  "abstract": "We study a stochastic Navier-Stokes system in which the spatial modes of the transport noise evolve dynamically and are coupled to the resolved velocity. The model couples a Navier-Stokes stochastic PDE to an infinite family of linearized Navier-Stokes equations for the noise correlation modes. These latter equations may contain a hyperviscosity. We prove existence of martingale solutions in two dimensions for hyperviscosity exponent s ≥ 1, and pathwise uniqueness for s > 1 under additional regularity of the initial noise modes. In three dimensions, we establish existence of martingale solutions for s > 3/2. The proof combines Galerkin approximations and compactness with estimates adapted to the coupled drift and stochastic terms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24396",
  "author_total": 3,
  "authors": [
    {
      "name": "Arnaud Debussche"
    },
    {
      "name": "Etienne Mémin"
    },
    {
      "name": "Sébastien Moskowitz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6h6ynb4s21x10.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24396",
  "fulltext_url": null,
  "id": "6h6ynb4s21x10",
  "issns": [],
  "landing_url": "https://hal.science/hal-05759193v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214028773",
  "pdf_url": "https://hal.science/hal-05759193/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6h6ynb4s21x10.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "hal-05759193",
      "source": "hal",
      "url": "https://hal.science/hal-05759193v1"
    },
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24396",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24396"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Well-posedness of a stochastic Navier-Stokes system with dynamically coupled subgrid scales",
  "title_text": "Well-posedness of a stochastic Navier-Stokes system with dynamically coupled subgrid scales",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6h6ynb4s21x10",
  "venue": "HAL",
  "versions": []
}