{
  "abstract": "Blow-up in the self-dual Chern--Simons--Higgs equation has a rich multiscale structure, but the detailed theory has largely focused on the simple regime, where one entire profile resolves each concentration point. By contrast, non-simple blow-up is analytically more delicate: several interacting regular cores must be resolved simultaneously as they collapse toward a single vortex while remaining separated on their own scales. Because of this difficulty, the existence of such solutions has remained a long-standing open problem. To the best of our knowledge, we prove the first existence result for non-simple blow-up solutions of this equation, covering in particular the previously unresolved finite-height Chern--Simons regime. We also show that non-simple clusters have equal limiting core masses, a common profile type, and regular-polygon arrangements. We determine their possible total masses and derive a mass-gap criterion that rules out such blow-up for certain vortex configurations. Our quantitative profile and moment estimates for general finite-height clusters guide the design of the approximate solution and clarify the core interactions underlying the finite-height construction. A separate construction on the unit disk produces two mean-field cores along a sequence with varying Dirichlet traces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20042",
  "author_total": 2,
  "authors": [
    {
      "name": "Youngae Lee"
    },
    {
      "name": "Lei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnh68gc4m47sr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20042",
  "fulltext_url": null,
  "id": "bnh68gc4m47sr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20042",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213606202",
  "pdf_url": "https://arxiv.org/pdf/2609.20042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnh68gc4m47sr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20042"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Non-simple blow-up for the Chern--Simons--Higgs equation: A priori analysis and constructions",
  "title_text": "Non-simple blow-up for the Chern--Simons--Higgs equation: A priori analysis and constructions",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:43Z",
  "url": "https://research.draconitic.com/paper/bnh68gc4m47sr",
  "venue": "arXiv",
  "versions": []
}