{
  "id": "1005.1484",
  "version": "v3",
  "published": "2010-05-10T09:57:27.000Z",
  "updated": "2011-05-19T14:09:05.000Z",
  "title": "Strichartz Estimates for the Vibrating Plate Equation",
  "authors": [
    "Elena Cordero",
    "Davide Zucco"
  ],
  "comment": "18 pages, 4 figures, some misprints corrected",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\\\"odinger-type equations we show its close relation with the Schr\\\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-19T14:09:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35B65",
      "35Q40",
      "35B40"
    ],
    "keywords": [
      "strichartz estimates",
      "lvp equation",
      "stationary homogeneous vibrating plate equation",
      "homogeneous sobolev spaces appear",
      "close relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1484C"
    }
  }
}