{
  "id": "1411.2342",
  "version": "v1",
  "published": "2014-11-10T07:51:44.000Z",
  "updated": "2014-11-10T07:51:44.000Z",
  "title": "Local well-posedness of the multi-layer shallow-water model with free surface",
  "authors": [
    "Ronan Monjarret"
  ],
  "comment": "55 pages, 2 figures, Ph.D. work",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we address the question of the hyperbolicity and the local well- posedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in H^s(R^2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this model and prove a more general criterion of hyperbolicity and local well-posedness, under a particular asymptotic regime and a weak stratification assumptions of the densities and the velocities. Finally, we consider a new conservative multi-layer shallow water model, we prove the symmetrizability, the hyperbolicity and the local well-posedness and rely it to the basic multi-layer shallow water model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-10T07:51:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A15",
      "15A18",
      "35A07",
      "35L45",
      "35P15"
    ],
    "keywords": [
      "local well-posedness",
      "multi-layer shallow-water model",
      "free surface",
      "basic multi-layer shallow water model",
      "general criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.2342M"
    }
  }
}