{
  "abstract": "In this paper, the first in a series devoted to finite-time singularities of point-vortex systems in domains with boundaries, we establish the existence of finite-time interior collapse for three vortices in the upper half-plane $\\mathbb{H}^+$. Our approach treats the boundary-induced interactions as a perturbation of the classical self-similar Gröbli collapse in the full plane. Under suitable conditions on the vortex circulations and collapse profile, we prove the existence of a one-dimensional local strong stable manifold of the augmented rescaled system, which generates exact solutions in which three distinct vortices collapse simultaneously at any prescribed interior point $z^*\\in\\mathbb{H}^+$. Moreover, these solutions are asymptotically self-similar, with the characteristic square-root collapse rate $O(\\sqrt{T-t})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01014",
  "author_total": 1,
  "authors": [
    {
      "name": "Cheng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fmbnwfj4g6cr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01014",
  "fulltext_url": null,
  "id": "2fmbnwfj4g6cr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01014",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fmbnwfj4g6cr.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On the Finite-Time Singularities of Point-Vortex Systems I: The Half-Plane",
  "title_text": "On the Finite-Time Singularities of Point-Vortex Systems I: The Half-Plane",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/2fmbnwfj4g6cr",
  "venue": "arXiv",
  "versions": []
}