{
  "abstract": "We describe the linearized dynamics near the Lamb-Chaplygin dipole, a classical traveling solution of the two-dimensional Euler equations. Exploiting the Hamiltonian structure of the system together with its symmetries, we identify all possible sources of linear instability. For general perturbations in $L^1\\cap L^p$, $p>2$, growth can occur through two explicit mechanisms triggered by: {\\rm (i)} a nonzero circulation on the core of the dipole, and {\\rm (ii)} a nontrivial component along the generalized eigenvectors associated with the eigenvalue $0$. In particular, we completely classify the spectrum and the Jordan chains of the operator associated with the linear dynamics. Both mechanisms hint for a nonlinear dynamics that may drift along the symmetry-generated family of traveling dipoles without moving away from it.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.09775",
  "author_total": 2,
  "authors": [
    {
      "name": "Francesco Pio Numero"
    },
    {
      "name": "Paolo Ventura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7e921ddv2k778.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.09775",
  "fulltext_url": null,
  "id": "7e921ddv2k778",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.09775",
  "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"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7164047980",
  "pdf_url": "https://arxiv.org/pdf/2606.09775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7e921ddv2k778.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2606.09775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.09775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Linear Stability of the Lamb-Chaplygin Dipole",
  "title_text": "Linear Stability of the Lamb-Chaplygin Dipole",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/7e921ddv2k778",
  "venue": "arXiv",
  "versions": []
}