{
  "abstract": "We establish a sharp uniqueness--nonuniqueness criterion for the two-dimensional incompressible Euler equations within a class of stationary arrays of disjoint neutral vortices. Let $Θ$ be any finite nondecreasing envelope for the vorticity $L^p$ norms, and set $I_Θ=\\int_{p_0}^\\infty Θ(p)^{-1}\\,dp$. If $I_Θ=\\infty$, every array in the corresponding class admits a unique Euler evolution, even among bounded energy-admissible weak velocity solutions. If $I_Θ<\\infty$, there exists a compactly supported array in the same class admitting two distinct unforced Lagrangian Euler evolutions from the same initial datum. The criterion holds for arbitrary nondecreasing envelopes $Θ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40552",
  "author_total": 4,
  "authors": [
    {
      "name": "Thomas Y. Hou"
    },
    {
      "name": "Xiang Qin"
    },
    {
      "name": "Peicong Song"
    },
    {
      "name": "Wenhan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agdyzqwts2c58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40552",
  "fulltext_url": null,
  "id": "agdyzqwts2c58",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40552",
  "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/2610.40552",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agdyzqwts2c58.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40552",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40552"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Sharp Uniqueness-Nonuniqueness Dichotomy for Neutral Vortex Arrays in $2$D Euler Equations",
  "title_text": "A Sharp Uniqueness-Nonuniqueness Dichotomy for Neutral Vortex Arrays in $2$D Euler Equations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/agdyzqwts2c58",
  "venue": "arXiv",
  "versions": []
}