{
  "abstract": "We construct real-valued solutions of the defocusing energy-supercritical nonlinear wave equation $\\partial_t^2u-Δu+u^p=0$ that blow up in finite time from smooth, compactly supported initial data. We consider three cases: for $p=3$ we construct blow-up solutions in all dimensions $d\\geq 9$, for $p=5$ we treat all dimensions $d\\geq 7$, while for $p=7$ we treat all dimensions $d\\geq 6$. The solutions we construct here appear to be the first blow-up solutions of defocusing energy-supercritical nonlinear wave equations with smooth real-valued data. The main step is the construction of nonzero \\emph{discretely self-similar profiles} that are periodic in self-similar time and real-analytic across the light cone. We find approximate profiles by numerical continuation from rotating self-similar solutions of the complex-valued equation and upgrade them to exact solutions by a computer-assisted Newton--Kantorovich argument in a Banach algebra of Fourier--Chebyshev coefficients. The main analytic ingredients are an exact description of the linear mode operators and uniform bounds for their inverses. The codes for the computer-assisted parts of the proofs, together with the approximate solutions, are available on GitHub \\cite{code}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06678",
  "author_total": 3,
  "authors": [
    {
      "name": "Matthieu Cadiot"
    },
    {
      "name": "Alexandru D. Ionescu"
    },
    {
      "name": "Stan Palasek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2tch9at3srmds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06678",
  "fulltext_url": null,
  "id": "2tch9at3srmds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06678",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7220714583",
  "pdf_url": "https://arxiv.org/pdf/2610.06678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2tch9at3srmds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.06678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-time blow-up for the real-valued defocusing energy-supercritical NLW",
  "title_text": "Finite-time blow-up for the real-valued defocusing energy-supercritical NLW",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/2tch9at3srmds",
  "venue": "arXiv",
  "versions": []
}