{
  "abstract": "We study SPDEs associated with $2$D active scalars driven by incompressible transport noise of Kraichnan type, with regularity exponent $α\\in (0,1)$; our examples include the Euler, SQG and IPM systems. We investigate whether a number of ``turbulent'' phenomenologies, which are well understood in the linear Kraichnan model, persist in this nonlinear setting, uniformly in vanishing viscosity approximations. First, for suitable values of $α$ and initial data in $L^p_x$, we establish anomalous regularization estimates, measured in appropriate endpoint Besov-type spaces of regularity $β=β(α,p)>0$. Remarkably, these results allow for some scaling supercritical regimes of the parameters $α,p$; on the other hand, for (sub)critical parameters, we recover the same regularity exponent $β=1-α$ as in the linear case. Second, in the (sub)critical case, we further prove anomalous integrability, namely solutions becoming instantaneously $L^\\infty_x$-valued at positive times, uniformly in the viscosity; moreover, in this case we establish strong existence and pathwise uniqueness of solutions to the inviscid SPDE, which are recovered as the unique vanishing viscosity limit. Finally, in the $2$D Euler case, for $α\\in (0,1/2)$, we establish anomalous dissipation of enstrophy and sharpness of anomalous regularization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25897",
  "author_total": 3,
  "authors": [
    {
      "name": "Lucio Galeati"
    },
    {
      "name": "Eliseo Luongo"
    },
    {
      "name": "Umberto Pappalettera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b049q7z79nj5k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25897",
  "fulltext_url": null,
  "id": "b049q7z79nj5k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25897",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214084254",
  "pdf_url": "https://arxiv.org/pdf/2609.25897",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b049q7z79nj5k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25897",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25897"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Anomalous properties of 2D active scalars perturbed by rough transport noise",
  "title_text": "Anomalous properties of 2D active scalars perturbed by rough transport noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/b049q7z79nj5k",
  "venue": "arXiv",
  "versions": []
}