{
  "abstract": "We consider a strongly dispersive Boussinesq-type system arising as a model for the propagation of weakly nonlinear water waves. The system is characterized by a nonlinearity parameter $0<ε\\le 1$ and a shallow water parameter $0<μ\\le 1$. In the Boussinesq regime $μ\\sim ε$, Saut, Wang and Xu \\cite{SWX2017} used a hyperbolic approach to prove the well-posedness of the system on a time scale of order $1/ε$, in both one and two dimensions, under a non-cavitation condition. In this paper, we establish well-posedness on a time scale of order $ ( μ^{ 1/4} ε^{-1} h_0 )^{4/3}$ in one dimension and of order $(μ^{ 1/4}ε^{-1} h_0)^{2-}$ in two dimensions, assuming a non-cavitation condition with a parameter $h_0>0$. Our results show quantitatively how the lifespan depends on the balance between nonlinearity and dispersion in the regimes $ε\\lesssim μ$ and $μ\\llε$. They also make explicit how the existence time deteriorates as $h_0\\to0$, that is, as the wave approaches cavitation. Our proofs combine dispersive and Strichartz estimates with energy estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39891",
  "author_total": 2,
  "authors": [
    {
      "name": "Achenef Tesfahun"
    },
    {
      "name": "Sigmund Selberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aeta7aqe2ztah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39891",
  "fulltext_url": null,
  "id": "aeta7aqe2ztah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39891",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7215048057",
  "pdf_url": "https://arxiv.org/pdf/2609.39891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aeta7aqe2ztah.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.39891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Improved existence time for a Boussinesq system",
  "title_text": "Improved existence time for a Boussinesq system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/aeta7aqe2ztah",
  "venue": "arXiv",
  "versions": []
}