{
  "abstract": "These notes present the construction in \\cite{euler} of finite-time blowup for the three-dimensional incompressible, unforced Euler equations on $\\mathbb R^3$: \\begin{equation} \\partial_tu+(u\\cdot\\nabla)u+\\nabla p=0,\\qquad \\nabla\\cdot u=0. \\end{equation} The construction successively adds oscillatory layers to smooth parent solutions. Each layer is constructed by a finite expansion and an exact correction, so that the resulting child solves Euler.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02509",
  "author_total": 1,
  "authors": [
    {
      "name": "Fan Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0arktmxfqghpy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02509",
  "fulltext_url": null,
  "id": "0arktmxfqghpy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02509",
  "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": "W7220409167",
  "pdf_url": "https://arxiv.org/pdf/2610.02509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0arktmxfqghpy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-time blowup of the Euler equation without forcing",
  "title_text": "Finite-time blowup of the Euler equation without forcing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/0arktmxfqghpy",
  "venue": "arXiv",
  "versions": []
}