{
  "abstract": "In the present paper, our primary focus is on the Boussinesq equations with fractional velocity dissipation $Λ^αu$ and temperature diffusion $Λ^βθ$. On the critical balance line $α+β=1$, establishing global regularity for weak velocity dissipation has been obstructed by the quadratic convective-buoyancy feedback, and all available results below $α=\\frac{10}{13}$ require a smallness assumption on the initial temperature. In this paper, we prove large-data global regularity across the extended regime $α>\\frac{\\sqrt{57}-5}{4} \\approx 0.637$. This provides a step beyond the previous barrier $α=\\frac{10}{13}$, unconditionally dismantling the temperature smallness assumption that has persisted in the literature for over a decade. The mathematical mechanism relies on a high-order Quadratic Normal Form transformation $H=ω-R_αθ-\\Bop(θ,θ)$ tailored to eliminate non-resonant quadratic vorticity-temperature interactions. Crucially, by uncovering the exact physical scalings of the underlying multilinear commutators and maintaining sharp fractional conjugates in the $L^m$-energy framework, we ensure that the global energy closure is governed entirely by the quadratic thermal dissipation. Once an integrability threshold $m>\\frac{2}α$ is attained, a fine Littlewood-Paley transport estimate drives a fractional regularity gain $H \\in B_{r,\\infty}^{3α-2}$, ensuring the velocity field achieves critical drift regularity $C^α$. By Silvestre-type drift regularization, this spontaneously generates positive Hölder continuity for the temperature, which in turn elevates the drift regularity strictly beyond the critical threshold, unlocking non-local Schauder estimates to prevent finite-time singularity formation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08765",
  "author_total": 4,
  "authors": [
    {
      "name": "Qian Li"
    },
    {
      "name": "Jiahong Wu"
    },
    {
      "name": "Xiaojing Xu"
    },
    {
      "name": "Zhuan Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7dqs88w9hfqx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08765",
  "fulltext_url": null,
  "id": "d7dqs88w9hfqx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08765",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08765",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7dqs88w9hfqx.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08765",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08765"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global regularity of the two-dimensional fractional Boussinesq equations with critical dissipation",
  "title_text": "Global regularity of the two-dimensional fractional Boussinesq equations with critical dissipation",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/d7dqs88w9hfqx",
  "venue": "arXiv",
  "versions": []
}