{
  "abstract": "This paper investigates the 2D quasilinear wave equation $\\displaystyle\\sum_{α,β=0}^{2}g^{αβ}(\\partialϕ)\\partial_{αβ}^{2}ϕ=0$ with the short pulse initial data $(ϕ, \\partial_tϕ)|_{t=1}=(δ^{2-\\varepsilon_0}ϕ_0(\\frac{r-1}δ,ω), δ^{1-\\varepsilon_0}ϕ_1(\\frac{r-1}δ,ω))$, where $0<\\varepsilon_0<1$ is a fixed constant and $δ>0$ is a small parameter. In our previous work [Ding Bingbing, Xin Zhouping, Yin Huicheng, Sci. China Math., Vol. 69 (2026), No. 3, 667-736], we have established the global existence of a smooth solution $ϕ$ under the $k$-th order null condition ($k\\ge 2$) when the $(k+1)$-th order null condition fails, provided that $0<\\varepsilon_0<\\varepsilon_k^*=\\frac{k}{k+1}$. As a natural continuation, the present paper demonstrates that for $\\varepsilon_0\\ge \\varepsilon_k^*$, the smooth solution $ϕ$ blows up in finite time. Consequently, the threshold $\\varepsilon_0=\\varepsilon_k^*$ is shown to be the critical exponent that precisely characterizes the global existence and finite-time blowup for smooth short pulse solutions to the aforementioned 2D quasilinear wave equation, under the assumption that the $k$-th order null condition holds while the $(k+1)$-th order null condition does not. A key novelty of our approach lies in deriving sharp orders of $δ$ for almost all quantities in both energy and pointwise estimates. This is achieved by utilizing the higher-order null structure in conjunction with a new good unknown recently introduced by us and the transport equation for the difference between this good unknown and its corrector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18358",
  "author_total": 3,
  "authors": [
    {
      "name": "Bingbing Ding"
    },
    {
      "name": "Zhouping Xin"
    },
    {
      "name": "Huicheng Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03waegh4t3dpd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18358",
  "fulltext_url": null,
  "id": "03waegh4t3dpd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18358",
  "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": "W7221833499",
  "pdf_url": "https://arxiv.org/pdf/2610.18358",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03waegh4t3dpd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18358",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18358"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Blowup of smooth solutions to 2D quasilinear wave equations with higher-order null conditions and short pulse initial data",
  "title_text": "Blowup of smooth solutions to 2D quasilinear wave equations with higher-order null conditions and short pulse initial data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/03waegh4t3dpd",
  "venue": "arXiv",
  "versions": []
}