{
  "abstract": "The primitive equations widely approximate the Navier--Stokes equations in large-scale geophysical fluid dynamics. Their finite-time singularity formation-which occurs exclusively in the inviscid case-sheds light on the mechanisms driving small-scale creation. Building on \\cite{Collot2023}, which constructed 2D horizontally odd solutions where the on-axis derivative $\\partial_X u(t,0,Z)$ blows up at rate $(T-t)^{-1}$ with boundary concentration scale $|\\ln (T-t)|^{-1}$, this paper characterizes this blow-up as forming between hyperbolic stagnation points. We derive precise asymptotic expansions for on-axis derivatives beyond leading order, identifying a horizontal concentration scale of $(T-t)^{3/2}$ characteristic of generic Burgers' singularities. Furthermore, we justify the 2D solution's expansion near the symmetry axis by proving $(T-t)^{3/2}$ is a universal lower bound on the radius of analyticity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28403",
  "author_total": 3,
  "authors": [
    {
      "name": "Charles Collot"
    },
    {
      "name": "Slim Ibrahim"
    },
    {
      "name": "Lingjun Qian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f7f9jf6y5a1g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28403",
  "fulltext_url": null,
  "id": "7f7f9jf6y5a1g",
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  "landing_url": "https://arxiv.org/abs/2610.28403",
  "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": "W7223095906",
  "pdf_url": "https://arxiv.org/pdf/2610.28403",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7f7f9jf6y5a1g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28403",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28403"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Near-blowup asymptotic analysis and analytical extension for the inviscid primitive equations",
  "title_text": "Near-blowup asymptotic analysis and analytical extension for the inviscid primitive equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/7f7f9jf6y5a1g",
  "venue": "arXiv",
  "versions": []
}