{
  "id": "1001.2850",
  "version": "v1",
  "published": "2010-01-16T19:47:16.000Z",
  "updated": "2010-01-16T19:47:16.000Z",
  "title": "Derivation and analysis of a new 2D Green-Naghdi system",
  "authors": [
    "Samer Israwi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard $2D $ Green-Naghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green-Naghdi equations. Using this property, we show that the solution of these new equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition. Finally, we prove that the new Green-Naghdi equations conserve the almost irrotationality of the vertically averaged horizontal component of the velocity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-16T19:47:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "2d green-naghdi system",
      "derivation",
      "green-naghdi equations conserve",
      "standard picard iterative scheme",
      "usual green-naghdi equations"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/23/11/009",
      "journal": "Nonlinearity",
      "year": 2010,
      "month": "Nov",
      "volume": 23,
      "number": 11,
      "pages": 2889
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010Nonli..23.2889I"
    }
  }
}