{
  "abstract": "We provide evidence of a finite-time singularity in the 3D Euler equations on the unbounded domain. Using a physics-informed neural network (PINN) with a self-similar ansatz, we find an approximate singular profile for the Euler system at the critical blowup rate of $0.5$ and certify it using a spline representation. The transport field associated with the obtained profile has local outgoing property throughout the domain that suggests linear damping, a key stabilizing mechanism for the candidate profile. We also establish a framework for proving nonlinear stability of the approximate self-similar profile, reducing the analysis to a large but finite collection of explicit estimates and computable constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10867",
  "author_total": 3,
  "authors": [
    {
      "name": "Adarsh Ganeshram"
    },
    {
      "name": "Valentin Duruisseaux"
    },
    {
      "name": "Anima Anandkumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6gmxbcwywr578.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10867",
  "fulltext_url": null,
  "id": "6gmxbcwywr578",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10867",
  "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": "W7212297673",
  "pdf_url": "https://arxiv.org/pdf/2609.10867",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6gmxbcwywr578.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.10867",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10867"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Self-Similar Singularity of the Euler Equations on $\\mathbb{R}^3$",
  "title_text": "Self-Similar Singularity of the Euler Equations on ℝ^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/6gmxbcwywr578",
  "venue": "arXiv",
  "versions": []
}