{
  "abstract": "By adapting the techniques used in the IPM blowup result of Córdoba-Martínez-Zoroa with spatially smooth force, we prove finite-time blow-up for the IPM equation on $\\mathbb T^2$ with a uniformly spacetime smooth force. In particular, we show there exist a smooth odd initial density, a smooth odd force $F\\in C^\\infty([0,1]\\times\\mathbb T^2)$, and a classical solution $ρ$ on $[0,1)$ whose density gradient and spatial velocity gradient diverge in $L^\\infty$ as $t\\uparrow 1$. Nevertheless, $ρ(t)$ converges in $C^η$ for every $0\\leqη<1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16470",
  "author_total": 3,
  "authors": [
    {
      "name": "Levent Alpöge"
    },
    {
      "name": "Tristan Buckmaster"
    },
    {
      "name": "Matei P. Coiculescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7q7g6d3yk2nkm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16470",
  "fulltext_url": null,
  "id": "7q7g6d3yk2nkm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16470",
  "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": "W7213430106",
  "pdf_url": "https://arxiv.org/pdf/2609.16470",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7q7g6d3yk2nkm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16470",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16470"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Extending the Córdoba-Martínez-Zoroa IPM Blow-Up to Uniformly Space-Time Smooth Forcing",
  "title_text": "Extending the Córdoba-Martínez-Zoroa IPM Blow-Up to Uniformly Space-Time Smooth Forcing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/7q7g6d3yk2nkm",
  "venue": "arXiv",
  "versions": []
}