{
  "abstract": "We consider the focusing mass-critical inhomogeneous biharmonic nonlinear Schrödinger equation \\[ i\\partial_tu=Δ^2u-|x|^{-b}|u|^{\\frac{8-2b}{N}}u, \\quad 0<b<\\min\\{4,N/2\\}. \\] We prove that every $H^2(\\mathbb R^N)$ solution with negative energy blows up in finite time, both forward and backward. No radial symmetry or finite-variance assumption is required. In particular, this rules out the global grow-up scenario in the previously known negative-energy blow-up alternative and establishes finite-time blow-up in the genuinely nonradial setting. The proof relies on a new localized virial argument exploiting the spatial inhomogeneity to control the localization errors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24244",
  "author_total": 2,
  "authors": [
    {
      "name": "Ngoc Uyen Cong Nguyen"
    },
    {
      "name": "Van Duong Dinh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40bffared9z4t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24244",
  "fulltext_url": null,
  "id": "40bffared9z4t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24244",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7223068200",
  "pdf_url": "https://arxiv.org/pdf/2610.24244",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40bffared9z4t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24244",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24244"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nonradial Finite-Time Blow-up for the Mass-Critical Inhomogeneous Biharmonic NLS",
  "title_text": "Nonradial Finite-Time Blow-up for the Mass-Critical Inhomogeneous Biharmonic NLS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/40bffared9z4t",
  "venue": "arXiv",
  "versions": []
}