{
  "id": "0908.3255",
  "version": "v2",
  "published": "2009-08-22T14:24:18.000Z",
  "updated": "2009-10-08T21:55:30.000Z",
  "title": "Strichartz estimates for the water-wave problem with surface tension",
  "authors": [
    "Hans Christianson",
    "Vera Mikyoung Hur",
    "Gigliola Staffilani"
  ],
  "comment": "Fixed typos and mistakes. Merged with arXiv:0809.4515",
  "categories": [
    "math.AP"
  ],
  "abstract": "Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales depending on the size of the frequencies. We infer that a solution $u$ of the dispersive equation we introduce satisfies local-in-time Strichartz estimates with loss in derivative: \\[ \\| u \\|_{L^p([0,T]) W^{s-1/p,q}(\\mathbb{R})} \\leq C, \\qquad \\frac{2}{p} + \\frac{1}{q} = {1/2}, \\] where $C$ depends on $T$ and on the norms of the initial data in $H^s \\times H^{s-3/2}$. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-08T21:55:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B15"
    ],
    "keywords": [
      "surface tension",
      "water-wave problem",
      "satisfies local-in-time strichartz estimates",
      "one-dimensional surface water-waves",
      "dispersion estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.3255C"
    }
  }
}