{
  "abstract": "We prove that all excited states $-\\sin(nx)$, $n\\geq2$, of the De Gregorio equation on the torus are nonlinearly unstable in the sense of Hadamard. More precisely, perturbations arbitrarily small in $H^2$ leave a fixed $H^1$ neighborhood of the state. For every $n\\geq2$, the linearized operator has a real eigenvalue $λ_n\\in(0.56,0.6)$. To prove this, we transform the eigenvalue problem into a Fuchsian equation on the complex disk and obtain a matching condition for the eigenvalue. This condition is verified rigorously using interval arithmetic. The nonlinear instability follows from a bootstrap argument in the spirit of Guo, Hallstrom, and Spirn.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03287",
  "author_total": 1,
  "authors": [
    {
      "name": "Miguel M. G. Pascual-Caballo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqevqga7wcr8j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03287",
  "fulltext_url": null,
  "id": "cqevqga7wcr8j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03287",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.03287",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqevqga7wcr8j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03287",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03287"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the instability of De Gregorio excited states",
  "title_text": "On the instability of De Gregorio excited states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/cqevqga7wcr8j",
  "venue": "arXiv",
  "versions": []
}