{
  "abstract": "We show that singularities of the three-dimensional cubic complex Ginzburg-Landau equation developing from smooth initial data can induce non-uniqueness of solutions after the time of blowup. The solutions we study start as backward self-similar solutions, and the source of the non-uniqueness is an unstable eigenvalue of the linearization around the forward self-similar profile generated by the singularity. We establish the existence of this eigenvalue, and hence the non-uniqueness, by a computer-assisted proof for specific values of the parameters in the equation. The work is in part motivated by similarities to conjectured behavior for the Navier-Stokes equation, with which the complex Ginzburg-Landau equation shares several important properties, such as an energy inequality and the scaling symmetry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08985",
  "author_total": 2,
  "authors": [
    {
      "name": "Joel Dahne"
    },
    {
      "name": "Vladimír Šverák"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5zb70107yrn2x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08985",
  "fulltext_url": null,
  "id": "5zb70107yrn2x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08985",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212086481",
  "pdf_url": "https://arxiv.org/pdf/2609.08985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5zb70107yrn2x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08985"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Non-uniqueness for the Complex Ginzburg-Landau Equation",
  "title_text": "Non-uniqueness for the Complex Ginzburg-Landau Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/5zb70107yrn2x",
  "venue": "arXiv",
  "versions": []
}