{
  "abstract": "We consider a Whitham-Boussinesq type system with surface tension arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves in shallow water, which is characterized by a nonlinearity parameter $0<ε\\le 1$, a shallow water parameter $0<μ\\le 1$ and a nonnegative surface tension parameter $β$. In this paper, we establish well-posedness of the associated Cauchy problem for $β>1/3$ on a time scale of order $ ( β_\\ast^{ 1/4} μ^{ 1/4} h_0 ε^{-1} )^{4/3}$ in one dimension and of order $( β_\\ast^{ 1/4} μ^{ 1/4} h_0 ε^{-1})^{2-}$ in two dimensions, where $β_\\ast= \\min(|3β-1|, 1/2)$, assuming a non-cavitation condition with a parameter $h_0>0$. In addition, we established well-posedness for the classical Whitham equation with either $β=0$ or $β>1/3$ on the timescale of order $ ( β_\\ast^{ 1/4} μ^{ 1/4} ε^{-1} )^{4/3}$. These results explicitly capture how the existence time depends on all the parameters involved. Our proofs rely on dispersive and Strichartz estimates combined with energy estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23612",
  "author_total": 2,
  "authors": [
    {
      "name": "Madina Kamet"
    },
    {
      "name": "Achenef Tesfahun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3m3q2fds4vs87.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23612",
  "fulltext_url": null,
  "id": "3m3q2fds4vs87",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23612",
  "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": "W7214003787",
  "pdf_url": "https://arxiv.org/pdf/2609.23612",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3m3q2fds4vs87.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23612",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23612"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Enhanced lifespan of solutions to Whitham-Boussinesq system with surface tension",
  "title_text": "Enhanced lifespan of solutions to Whitham-Boussinesq system with surface tension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/3m3q2fds4vs87",
  "venue": "arXiv",
  "versions": []
}