{
  "abstract": "We construct an odd smooth initial density for the unforced incompressible porous media (IPM) equation on $\\mathbb T^2$ whose solution develops a finite-time blowup. The components $\\partial_{x_2}ρ(t,0)$ and $\\partial_{x_1}u_1(t,0)$ tend to $+\\infty$ as the maximal smooth existence time is approached, while the density and velocity remain bounded in $L^2$. Starting from a stationary solution, we iterate the angular amplification of localized oscillations with rapidly growing frequencies, adapting the mechanism of Córdoba and Martínez-Zoroa [7] for forced IPM. Each perturbation is constructed from time zero and creates the geometry configuration for the next iteration stage. A one-sided upper bound for the pressure Hessian is applied to control backward preparation and initial perturbations, following an idea from the Euler construction of OpenAI [14].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06712",
  "author_total": 1,
  "authors": [
    {
      "name": "Mimi Dai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5pr0hwb6vfj6v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06712",
  "fulltext_url": null,
  "id": "5pr0hwb6vfj6v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06712",
  "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": "W7220730937",
  "pdf_url": "https://arxiv.org/pdf/2610.06712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5pr0hwb6vfj6v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06712"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-time blowup for 2D unforced IPM",
  "title_text": "Finite-time blowup for 2D unforced IPM",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/5pr0hwb6vfj6v",
  "venue": "arXiv",
  "versions": []
}