{
  "abstract": "We study the stochastic Córdoba--Córdoba--Fontelos equation driven by multiplicative Stratonovich noise. The noise amplitude is allowed to be a pseudo-differential operator whose leading part is nearly skew-adjoint. This class contains classical transport noise and also permits genuinely nonlocal perturbations. We first develop a local-in-time theory for maximal classical solutions in Sobolev spaces, proving existence, uniqueness, and a blow-up criterion. We then consider the special case of Stratonovich transport. For sufficiently large initial nonlocal steepness at a global maximum, we prove finite-time blow-up with arbitrarily high prescribed probability and obtain an explicit upper bound on the lifespan. Finally, on the event that the nonlocal steepness at the transported maximum diverges, we establish a conditional Type-I upper bound. When the terminal Cesàro average of the normalised nonlocal energy converges, we further identify the exact leading-order blow-up rate in terms of its limiting value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02019",
  "author_total": 4,
  "authors": [
    {
      "name": "Diego Alonso-Orán"
    },
    {
      "name": "Rafael Granero-Belinchón"
    },
    {
      "name": "Yingting Miao"
    },
    {
      "name": "Hao Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pa2cxgbe7xzx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02019",
  "fulltext_url": null,
  "id": "8pa2cxgbe7xzx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02019",
  "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": "W7207566456",
  "pdf_url": "https://arxiv.org/pdf/2609.02019",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pa2cxgbe7xzx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02019",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02019"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Pseudo-differential noise and nonlocal singularity formation in the stochastic Córdoba--Córdoba--Fontelos equation",
  "title_text": "Pseudo-differential noise and nonlocal singularity formation in the stochastic Córdoba--Córdoba--Fontelos equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/8pa2cxgbe7xzx",
  "venue": "arXiv",
  "versions": []
}