{
  "abstract": "We study radially symmetric solutions to the three-dimensional semilinear wave system with distinct propagation speeds \\[ u_{tt}-c_1^2Δu=|v_t|^p\\ , \\ v_{tt}-c_2^2Δv=|u_t|^q\\ , \\ c_1, c_2>0\\ , c_1\\neq c_2\\ . \\] For \\(1<p,q<2\\), we prove that \\[ Γ(p,q) = 2+\\max\\left\\{\\frac1p,\\frac1q\\right\\}-pq=0 \\] is the exact critical curve separating small-data global existence from finite-time blow-up. More precisely, sufficiently small, compactly supported radial initial data give rise to global solutions when $Γ(p,q)<0$. On the other hand, for a class of initial data, the corresponding solutions blow up in finite time, with an upper bound for the lifespan, when $Γ(p,q)\\geq 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07710",
  "author_total": 3,
  "authors": [
    {
      "name": "Wei Dai"
    },
    {
      "name": "Mengyun Liu"
    },
    {
      "name": "Chengbo Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eka569zmw15aq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07710",
  "fulltext_url": null,
  "id": "eka569zmw15aq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07710",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07710",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eka569zmw15aq.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07710",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07710"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Critical Curve for Three-Dimensional Radial Wave Systems with Distinct Speeds",
  "title_text": "Critical Curve for Three-Dimensional Radial Wave Systems with Distinct Speeds",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/eka569zmw15aq",
  "venue": "arXiv",
  "versions": []
}