{
  "abstract": "For 3-D quadratic quasilinear wave equations in exterior domains with homogeneous Dirichlet boundary conditions and small initial data of size $\\varepsilon>0$, the authors of two papers [M. Keel, H. Smith, C.D. Sogge, Amer. J. Math. 122 (2000), no. 4, 805-842; J. Amer. Math. Soc. 17 (2004), no. 1, 109-153] have shown that the lifespan ${\\bar T}_{\\varepsilon}$ of smooth solutions satisfies ${\\bar T}_{\\varepsilon}=\\infty$ or ${\\bar T}_{\\varepsilon}\\ge e^{C/\\varepsilon}$, depending on whether the null condition holds or not, respectively. However, for the corresponding 2-D problem in exterior domains, it remains a difficult and unsolved problem to determine the precise lifespan $T_{\\varepsilon}$ of smooth solutions. In our previous papers, we have established that $T_{\\varepsilon}=\\infty$ holds when both the first and second null conditions are satisfied; and that $T_{\\varepsilon}\\ge\\frac{C}{\\varepsilon^2}$ holds when the first null condition is violated. In this paper, we will prove $T_{\\varepsilon}\\ge e^{C/\\varepsilon^2}$ when the first null condition holds but the second null condition is violated. Combining these results, we have systematically established sharp estimates for the lifespan $T_{\\varepsilon}$ of 2-D quadratic quasilinear wave equations in exterior domains with homogeneous Dirichlet boundary conditions. Moreover, our series of results for quasilinear wave equations in 2-D exterior domains are consistent with the corresponding results for the classical Cauchy problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01471",
  "author_total": 2,
  "authors": [
    {
      "name": "Fei Hou"
    },
    {
      "name": "Huicheng Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bj06e0fsscfx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01471",
  "fulltext_url": null,
  "id": "4bj06e0fsscfx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01471",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bj06e0fsscfx.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Almost global solutions of 2-D quadratic quasilinear wave equations in exterior domains without the second null condition",
  "title_text": "Almost global solutions of 2-D quadratic quasilinear wave equations in exterior domains without the second null condition",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/4bj06e0fsscfx",
  "venue": "arXiv",
  "versions": []
}