{
  "abstract": "We study existence and uniqueness for the 2D incompressible Euler equations on infinite sectors of acute angle $β$, focusing on vorticity in Hölder-type spaces. In the inifinite sectors, for every $β$, H\"older regularity cannot be expected without decay at infinity. Moreover, the corner causes Schauder-type estimates to fail at sufficiently high regularity. To address these difficulties, we introduce weighted H\"older spaces and establish well-posedness for every acute angle, without any decay assumption at infinity. These spaces include scale-invariant functions, allowing us to study their regularity and dynamics. We then apply this theory to standard $C^{k,α}$ spaces and show that $k+α=π/β-1$ is the well-posedness threshold. Above this threshold, we construct initial data that exhibit instantaneous loss of regularity. At the threshold, the problem is well-posed if and only if $π/β$ is not an integer. For well-posedness in $C^{k,α}$, we assume that the initial vorticity belongs to a weighted H\"older space rather than imposing decay at infinity. This class includes compactly supported initial vorticities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26315",
  "author_total": 1,
  "authors": [
    {
      "name": "Jaewan Choi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/deg1wv8k30nmp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26315",
  "fulltext_url": null,
  "id": "deg1wv8k30nmp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26315",
  "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",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7223070743",
  "pdf_url": "https://arxiv.org/pdf/2610.26315",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/deg1wv8k30nmp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26315",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26315"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-posedness threshold of the 2D Euler equations in Hölder spaces on infinite sectors",
  "title_text": "Well-posedness threshold of the 2D Euler equations in Hölder spaces on infinite sectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/deg1wv8k30nmp",
  "venue": "arXiv",
  "versions": []
}