{
  "abstract": "We prove persistence of $C^2$ boundary regularity for patch solutions of the two-dimensional aggregation transport equation, in contrast with the known $C^2$ ill-posedness of Euler vortex patches. More generally, we consider transport equations with kernels of the form $L(\\nabla N)$, where $N$ is the fundamental solution of the Laplacian and $L$ is a linear map. We show that $C^2$ regularity persists for every $C^2$ initial patch if and only if $L$ is a scalar multiple of the identity. Our approach builds on the curvature formulation introduced by Kiselev and Luo.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03258",
  "author_total": 2,
  "authors": [
    {
      "name": "Juan Carlos Cantero"
    },
    {
      "name": "Marc Magaña"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xx4q8eb4f1n3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03258",
  "fulltext_url": null,
  "id": "6xx4q8eb4f1n3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03258",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xx4q8eb4f1n3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Persistence of $C^2$ regularity for aggregation patches",
  "title_text": "Persistence of C^2 regularity for aggregation patches",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/6xx4q8eb4f1n3",
  "venue": "arXiv",
  "versions": []
}