{
  "abstract": "The inviscid generalized surface quasi-geostrophic (gSQG) equations are a family of active scalar equations parametrized by a scalar $α$ that includes the two-dimensional Euler equations ($α= 0)$ and the SQG equation $(α= 1)$. We prove that, for every $α\\in (\\frac{7}{4}, 2)$ and every $T > 0$, there exists a self-similar patch solution whose boundary is a smooth, unbounded graph for $0 \\leq t < T$ and develops a corner singularity at time $T$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32857",
  "author_total": 2,
  "authors": [
    {
      "name": "Javier Gomez-Serrano"
    },
    {
      "name": "Marcus Pasquariello"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0nw0v4wqm5gxc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32857",
  "fulltext_url": null,
  "id": "0nw0v4wqm5gxc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32857",
  "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",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7223652416",
  "pdf_url": "https://arxiv.org/pdf/2610.32857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0nw0v4wqm5gxc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32857"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Self-similar solutions for the gSQG patch equations",
  "title_text": "Self-similar solutions for the gSQG patch equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/0nw0v4wqm5gxc",
  "venue": "arXiv",
  "versions": []
}