{
  "abstract": "We study the three-dimensional defocusing cubic nonlinear wave equation with homogeneous Dirichlet boundary condition in the exterior of the unit ball, $Ω=\\R^3\\backslash\\overline{B(0,1)}$, for radial initial data. For every $\\frac12\\leq s\\leq\\frac34$, we establish global well-posedness in $\\dot H^s_{D,rad}(Ω)\\times\\dot H^{s-1}_{D,rad}(Ω)$, including the critical endpoint $s=\\frac12$, without an additional $L^4$ assumption on the initial displacement. The proof uses the distorted Fourier transform associated with the Dirichlet Laplacian to establish radial Sobolev embeddings, including the quantitative estimate $\\|f\\|_{L^p(Ω)}\\leq C\\sqrt p\\,\\|f\\|_{\\dot H_D^{1/2}(Ω)}$ for $4\\leq p<\\infty$, with $C$ independent of $p$. We combine a nonlinear Fourier truncation argument with the critical Strichartz estimate to construct a global nonlinear component with high-frequency-truncated initial data. For the remainder, we construct a local energy solution in an affine energy space and derive a logarithmic energy inequality that prevents finite-time energy blow-up. Persistence of the original Sobolev regularity, uniqueness, and local Lipschitz dependence on each finite time interval complete the proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38495",
  "author_total": 1,
  "authors": [
    {
      "name": "Ze Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2vws99752n6p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38495",
  "fulltext_url": null,
  "id": "b2vws99752n6p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38495",
  "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/2610.38495",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2vws99752n6p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38495",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38495"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Low-regularity global well-posedness for the defocusing cubic wave equation outside a ball with radial initial data",
  "title_text": "Low-regularity global well-posedness for the defocusing cubic wave equation outside a ball with radial initial data",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/b2vws99752n6p",
  "venue": "arXiv",
  "versions": []
}