{
  "abstract": "We study dual-cascade flux laws for the stochastic forced--dissipative surface quasi-geostrophic (SQG) equation on a large periodic box. For statistically stationary solutions, under a weak anomalous dissipation assumption, we derive rigorous mixed third-order structure-function laws for the dual cascade: a Yaglom-type law for the direct cascade of surface potential energy (SPE) and a mixed flux law for the inverse cascade of the Hamiltonian. We further establish complementary scaling laws: a cubic small-scale law for the Hamiltonian structure function and a large-scale vanishing law for the SPE structure function. In particular, both Hamiltonian laws appear to be new for SQG even as an explicit third-order structure-function relation. We also prove Onsager-type obstruction results showing that sufficiently regular stationary families cannot sustain the corresponding non-zero fluxes: $B^s_{3,\\infty}$-regularity above the Onsager threshold $1/3$ rules out the direct SPE flux, while sufficient low-frequency Besov regularity rules out the inverse Hamiltonian flux. These results provide a rigorous formulation of the SQG dual-cascade phenomenology in a stochastic stationary setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.26788",
  "author_total": 3,
  "authors": [
    {
      "name": "Rongchang Liu"
    },
    {
      "name": "Kening Lu"
    },
    {
      "name": "Zexin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/av2jaggvmjf8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.26788",
  "fulltext_url": null,
  "id": "av2jaggvmjf8z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.26788",
  "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"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7166053809",
  "pdf_url": "https://arxiv.org/pdf/2606.26788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/av2jaggvmjf8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2606.26788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.26788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Mixed Third-Order Flux Laws for Dual Cascade in the Stochastic SQG Equation",
  "title_text": "Mixed Third-Order Flux Laws for Dual Cascade in the Stochastic SQG Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/av2jaggvmjf8z",
  "venue": "arXiv",
  "versions": []
}