{
  "abstract": "We prove that non-uniqueness of weak solutions to the forced $$\\alpha $$ α -SQG equation with Sobolev regularity $$W^{s,p}$$ W s , p in the supercritical regime $$s < \\alpha + \\frac{2}{p}$$ s < α + 2 p , covering the 2D Euler equation ( $$\\alpha = 0$$ α = 0 ), the Surface Quasi-Geostrophic equation ( $$\\alpha = 1$$ α = 1 ), and the intermediate cases. A key step is the construction of smooth, compactly supported vortices that exhibit non-linear instability. As a by-product, we show that existence of global smooth solutions to the (unforced) $$\\alpha $$ α -SQG equation that are neither rotating nor traveling.",
  "abstract_shown": true,
  "affiliations": [
    "Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28049 Madrid, Spain",
    "Departamento de Matemáticas, Universidad Autónoma de Madrid, Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28049 Madrid, Spain",
    "Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany",
    "Departament d'Anàlisi Matemàtica, Universitat de València, 46100 Burjassot, Spain"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ángel Castro",
      "orcid": "0000-0002-6652-1963"
    },
    {
      "affs": [
        1
      ],
      "name": "Daniel Faraco",
      "orcid": "0000-0001-7860-9500"
    },
    {
      "affs": [
        2
      ],
      "name": "Francisco Mengual",
      "orcid": "0009-0009-9241-7105"
    },
    {
      "affs": [
        3
      ],
      "name": "Marcos Solera",
      "orcid": "0000-0001-7774-4516"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bcaydf12nyr5y.bib",
  "cited_by": 16,
  "doi": "10.1007/s00205-026-02252-x",
  "fulltext_url": null,
  "id": "bcaydf12nyr5y",
  "issns": [
    "0003-9527",
    "1432-0673"
  ],
  "landing_url": "https://doi.org/10.1007/s00205-026-02252-x",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W4407632801",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00205-026-02252-x.pdf",
  "pmcid": "PMC13633972",
  "pmid": "42830883",
  "published": "2026-10-03",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/bcaydf12nyr5y.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T13:20:36Z",
      "native_id": "W4407632801",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s00205-026-02252-x"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Navier-Stokes equation solutions",
      "subfield": "general"
    }
  ],
  "title": "Unstable Vortices, Sharp Non-Uniqueness with Forcing, and Global Smooth Solutions for the SQG Equation",
  "title_text": "Unstable Vortices, Sharp Non-Uniqueness with Forcing, and Global Smooth Solutions for the SQG Equation",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/bcaydf12nyr5y",
  "venue": "Archive for Rational Mechanics and Analysis",
  "versions": []
}