{
  "abstract": "This paper gives a readable and accessible version of the profile-construction part of OpenAI's manuscript \"Finite Time Blowup for Navier-Stokes\". We regard OpenAI's work as a major advance on the Navier-Stokes Millennium Prize Problem. The profiles are smooth and axi-symmetric. Inserting them into the Navier-Stokes equations gives a residual consisting of a divergence-form term and a remainder vanishing to infinite order in $1-t$ on fixed similarity sectors. The associated stress and radial shear satisfy the admissible cone condition. The stress need not be small. We introduce a new linear model that provides a clearer explanation of the inner core construction. The cancellation by oscillatory pulses will be treated in the companion paper \"Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses\".",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35406",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhen Lei"
    },
    {
      "name": "Xiao Ren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9psnk0vzrhxjn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35406",
  "fulltext_url": null,
  "id": "9psnk0vzrhxjn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35406",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214762479",
  "pdf_url": "https://arxiv.org/pdf/2609.35406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9psnk0vzrhxjn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35406"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder",
  "title_text": "Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/9psnk0vzrhxjn",
  "venue": "arXiv",
  "versions": []
}