{
  "abstract": "In this paper, we prove blowup for the defocusing septic complex-valued nonlinear wave equation in R 4 + 1 \\mathbb {R}^{4+1} . This work builds on the earlier results of Shao, Wei, and Zhang [Forum Math. Pi 13 (2025); Self-similar imploding solutions of the relativistic Euler equations , arXiv:2403.11471, 2024], reducing the order of the nonlinearity from 29 29 to 7 7 in R 4 + 1 \\mathbb {R}^{4+1} . As by Shao, Wei, and Zhang [Forum Math. Pi 13 (2025); Self-similar imploding solutions of the relativistic Euler equations , arXiv:2403.11471, 2024], the proof hinges on a connection between solutions to the nonlinear wave equation and the relativistic Euler equations via a front compression blowup mechanism. More specifically, the problem is reduced to constructing smooth, radially symmetric, self-similar imploding profiles for the relativistic Euler equations. As with implosion for the compressible Euler equations, the relativistic analogue admits a countable family of smooth imploding profiles. The result of Shao, Wei, and Zhang [ Self-similar imploding solutions of the relativistic Euler equations , arXiv:2403. 11471, 2024] represents the construction of the first profile in this family. In this paper, we construct a sequence of solutions corresponding to the higher-order profiles in the family. This allows us to saturate the inequalities necessary to show blowup for the defocusing complex-valued nonlinear wave equation with an integer order of nonlinearity and radial symmetry via this mechanism.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Tristan Buckmaster",
      "orcid": "0000-0001-6356-5699"
    },
    {
      "name": "Jiajie Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6j1p4zn3efd6j.bib",
  "cited_by": 10,
  "doi": "10.1090/cams/71",
  "fulltext_url": null,
  "id": "6j1p4zn3efd6j",
  "issns": [
    "2692-3688"
  ],
  "landing_url": "https://doi.org/10.1090/cams/71",
  "language": "en",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
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  "openalex": "W7168273867",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-14",
  "publisher": "American Mathematical Society",
  "ris": "https://research.draconitic.com/paper/6j1p4zn3efd6j.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W7168273867",
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      "url": "https://doi.org/10.1090/cams/71"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Advanced Mathematical Physics Problems",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Blowup for the defocusing septic complex-valued nonlinear wave equation in ℝ⁴⁺¹",
  "title_text": "Blowup for the defocusing septic complex-valued nonlinear wave equation in ℝ⁴⁺¹",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/6j1p4zn3efd6j",
  "venue": "Communications of the American Mathematical Society",
  "versions": []
}