{
  "id": "2201.03628",
  "version": "v2",
  "published": "2022-01-10T20:19:31.000Z",
  "updated": "2022-06-23T11:03:56.000Z",
  "title": "Long-time existence for a Whitham--Boussinesq system in two dimensions",
  "authors": [
    "Achenef Tesfahun"
  ],
  "comment": "18 ; To appear in Comm. Contemp. Math. arXiv admin note: text overlap with arXiv:2106.02717",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with a two dimensional Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem is well-posed for initial data of low regularity, with existence time of scale $\\mathcal O(1/\\sqrt{\\epsilon})$, where $\\epsilon>0$ is a shallowness parameter measuring the ratio of the amplitude of the wave to the mean depth of the fluid. The key ingredients in the proof are frequency loacalised dispersive and Strichartz estimates that depend on $\\epsilon$ as well as bilinear estimates in some Strichartz norms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-23T11:03:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-time existence",
      "dimensions",
      "dimensional whitham-boussinesq system modelling surface",
      "whitham-boussinesq system modelling surface waves",
      "inviscid incompressible fluid layer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}