{
  "abstract": "This work studies the three-dimensional incompressible Navier-Stokes equations through structural decomposition and normalized enstrophy-growth intervals. Starting from a hypothetical finite maximal smooth time T_* < infinity, first-hitting times are constructed at which the enstrophy doubles. Navier-Stokes scaling normalizes every such interval from enstrophy 1 to 2. For the normalized palinstrophy cost q_n and energy cost J_n, we derive the block estimate\n\nJ_n >= c_nu * (q_n + 1/2)^4 / q_n^3,\n\ntogether with weighted summability constraints and exact successive-scale relations. These imply that every hypothetical finite-time doubling cascade must satisfy\n\nintegral from t_n to T_* of ||grad omega(t)||_2^2 dt = infinity\n\nfor every n. Moreover, for the truncated terminal tails\n\nT_n^(N) = sum from k=0 to N of 2^k * q_(n+k),\n\nthe successive tails satisfy the exact relation\n\nT_n^(N) - q_n = 2 * T_(n+1)^(N-1),\n\nand hence\n\n(T_n^(N) - q_n) / T_(n+1)^(N-1) = 2\n\nfor every N >= 1. Thus, although both aligned terminal tails diverge as N -> infinity, their relative scale factor remains exactly preserved. The resulting scalar constraints remain mutually compatible and therefore do not exclude T_* < infinity. The argument yields necessary structural conditions for a hypothetical finite-time singularity, but does not establish global regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Son Tuyet Tran",
      "orcid": "0009-0007-9871-9871"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cn4zk6q6gcggz.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23493417",
  "fulltext_url": null,
  "id": "cn4zk6q6gcggz",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23493417",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23493417/files/Navier_Stokes_.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cn4zk6q6gcggz.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:19Z",
      "native_id": "23493417",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23493417"
    }
  ],
  "subjects": [],
  "title": "Solving the Three-Dimensional Incompressible Navier–Stokes Global Regularity Problem by Structural Decomposition and Normalized Growth Analysis",
  "title_text": "Solving the Three-Dimensional Incompressible Navier–Stokes Global Regularity Problem by Structural Decomposition and Normalized Growth Analysis",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:19Z",
  "url": "https://research.draconitic.com/paper/cn4zk6q6gcggz",
  "venue": "Zenodo",
  "versions": []
}