{
  "abstract": "We study global regularity and the infinite Prandtl number limit for temperature patches of the two-dimensional nondiffusive Boussinesq system on $\\mathbb R^2$, with velocity dissipation $Λ^{2α}$, $\\frac12<α\\leq1$. We establish global well-posedness for $θ_0\\in L^1\\cap L^\\infty$ and divergence-free $u_0\\in W^{1,p}$, $2\\leq p<\\infty$. Under suitable profile and striated regularity assumptions, we prove global persistence of $C^{1,γ}$ and $C^{2,γ}$ patch boundaries for every $0<γ\\leq1$, allowing nonconstant profiles and including the Lipschitz endpoints $W^{2,\\infty}$ and $W^{3,\\infty}$. The velocity gradient and boundary regularity estimates are uniform in $\\mathrm{Pr}\\in[1,\\infty)$ on each finite time interval. Uniform global $L^r$ velocity bounds hold for suitable finite $r$ when $α<1$, and at $α=1$ for zero-mean initial temperatures with finite first absolute moment. Such bounds fail at $α=1$ for compactly supported nonzero-mean data. For temperature patches, we justify the infinite Prandtl number limit in the original frame when $α<1$ or the initial temperature has zero mean, and in a moving frame otherwise. The limit is the unique normalized global weak solution of the (fractional) Stokes-transport system and, importantly, preserves the patch structure and boundary regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12253",
  "author_total": 3,
  "authors": [
    {
      "name": "Omar Lazar"
    },
    {
      "name": "Liutang Xue"
    },
    {
      "name": "Jiakun Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0b0hwnhevs4h9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12253",
  "fulltext_url": null,
  "id": "0b0hwnhevs4h9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12253",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7221081895",
  "pdf_url": "https://arxiv.org/pdf/2610.12253",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0b0hwnhevs4h9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12253",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12253"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global regularity and infinite Prandtl-number limit for 2D Boussinesq temperature patches in $W^{k,\\infty}$ and $C^{k,γ}$: lower-order case",
  "title_text": "Global regularity and infinite Prandtl-number limit for 2D Boussinesq temperature patches in W^k,∞ and C^k,γ: lower-order case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/0b0hwnhevs4h9",
  "venue": "arXiv",
  "versions": []
}