{
  "abstract": "We study the unforced viscous Katz--Pavlović dyadic model with non-negative smooth initial data for two shell settings. For super-exponential scales $N_n=N_0^{b^n}$, with $N_0>1$ and $1<b<2$, we prove that $α=1/(b+2)$ is the sharp dissipation threshold: every such datum produces a globally smooth solution at and above this value, whereas suitable compactly supported data lose regularity in finite time below it. For geometric scales $N_n=N_0Λ^n$, global regularity holds when $α\\geq1/3$ and $4α-1>(\\log2)/(2\\logΛ)$. In particular, for $Λ>2^{3/2}$, the result reaches $α=1/3$ and, together with the known classical blow-up theorem, identifies the sharp threshold in classical shell ratios.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21312",
  "author_total": 1,
  "authors": [
    {
      "name": "Ziqian Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8n2ca0gtkhetg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21312",
  "fulltext_url": null,
  "id": "8n2ca0gtkhetg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21312",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7213939350",
  "pdf_url": "https://arxiv.org/pdf/2609.21312",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8n2ca0gtkhetg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21312",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21312"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Regularity Thresholds for Viscous Katz--Pavlović Dyadic Models",
  "title_text": "Sharp Regularity Thresholds for Viscous Katz--Pavlović Dyadic Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/8n2ca0gtkhetg",
  "venue": "arXiv",
  "versions": []
}