{
  "abstract": "In this manuscript, we determine the critical exponent for the two-dimensional semilinear wave equation with strong damping. A recent result in D'Abbicco (arXiv, 2026) gives global in-time small data solutions for $p>\\frac{10}{3}$, whereas we in the paper prove finite-time blow-up for $2<p\\leqslant\\frac{10}{3}$ under an averaged sign condition on the initial velocity. Together with the previously known blow-up result for $1<p\\leqslant3$, the threshold for the power nonlinearity $|u|^p$ is \\begin{align*} p=p_{\\mathrm{crit}}=\\frac{10}{3}. \\end{align*} We prove positivity of the full two-dimensional velocity fundamental solution and construct a positive averaged kernel, which allows us to establish a nonlinear lower-bound iteration in a parabolic region.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01964",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenhui Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7k56jjmtxn9zb.bib",
  "cited_by": 1,
  "doi": "10.48550/arxiv.2609.01964",
  "fulltext_url": null,
  "id": "7k56jjmtxn9zb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01964",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7207753314",
  "pdf_url": "https://arxiv.org/pdf/2609.01964",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7k56jjmtxn9zb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01964",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01964"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The critical exponent for the two-dimensional semilinear wave equation with strong damping",
  "title_text": "The critical exponent for the two-dimensional semilinear wave equation with strong damping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/7k56jjmtxn9zb",
  "venue": "arXiv",
  "versions": []
}