{
  "abstract": "We consider the focussing cubic Klein-Gordon equation on $\\mathbb{R}^{3+1}$ in the radial setting. Foundational work by Nakanishi-Schlag gives a complete qualitative characterisation of the dynamics near the ground state $Q$, in particular revealing a threshold phenomenon, whereby a co-dimension one Lipschitz manifold separates finite time blow up from scattering solutions in forward time. Our aim in this paper is to derive an effective bound for the scattering norm $\\|u\\|_{L_t^3([0,\\infty);L_x^6(\\mathbb{R}^3))}$, for scattering energy class solutions $u$ with data sufficiently near $Q$ and close to the threshold manifold. This requires the development of an induction on energy strategy in a setting where an alternative to the usual Morawetz approach appears necessary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41718",
  "author_total": 2,
  "authors": [
    {
      "name": "Jaime Gómez"
    },
    {
      "name": "Joachim Krieger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3486xj7b8e72s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41718",
  "fulltext_url": null,
  "id": "3486xj7b8e72s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41718",
  "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/2610.41718",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3486xj7b8e72s.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41718",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41718"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Effective threshold dynamics for the cubic nonlinear Klein-Gordon equation in three dimensions",
  "title_text": "Effective threshold dynamics for the cubic nonlinear Klein-Gordon equation in three dimensions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/3486xj7b8e72s",
  "venue": "arXiv",
  "versions": []
}