{
  "abstract": "We prove instantaneous loss of Sobolev regularity across a fixed gap for the inviscid surface quasi-geostrophic equation on $\\mathbb R^2$. More precisely, for every $1<s<2$, $T>0$ and $\\varepsilon>0$, we construct initial data $θ_0\\in H^s(\\mathbb R^2)$ with $\\|θ_0\\|_{H^s}\\leq\\varepsilon$ that generate a solution $θ$ on $[0,T]$ such that \\[ θ\\in L^\\infty([0,T];H^{1+γ}(\\mathbb R^2)), \\quad θ(t)\\notin H^σ(\\mathbb R^2) \\quad\\text{for every }t\\in(0,T],\\ σ>σ_*(s), \\] where $γ>0$ and $σ_*(s)$ satisfy \\[ 1+γ<σ_*(s):= \\frac{s(3-s)}{1+2s-s^2}<s. \\] The solution is unique in a determined family of classical solutions with initial datum $θ_0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12011",
  "author_total": 3,
  "authors": [
    {
      "name": "Qionglei Chen"
    },
    {
      "name": "Changxing Miao"
    },
    {
      "name": "Yaowei Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bpppe215emtn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12011",
  "fulltext_url": null,
  "id": "6bpppe215emtn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12011",
  "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": "W7221121708",
  "pdf_url": "https://arxiv.org/pdf/2610.12011",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bpppe215emtn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12011",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12011"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Instantaneous gap loss of Sobolev regularity for the surface quasi-geostrophic equation",
  "title_text": "Instantaneous gap loss of Sobolev regularity for the surface quasi-geostrophic equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/6bpppe215emtn",
  "venue": "arXiv",
  "versions": []
}