{
  "id": "1911.01183",
  "version": "v1",
  "published": "2019-11-04T13:16:17.000Z",
  "updated": "2019-11-04T13:16:17.000Z",
  "title": "Blow up of fractional Schrödinger equations on manifolds with nonnegative Ricci curvature",
  "authors": [
    "Huali Zhang",
    "Shiliang Zhao"
  ],
  "comment": "10pages. Welcome all comments",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, the well-posedness of Cauchy's problem of fractional Schr\\\"odinger equations with a power type nonlinearity on manifolds with nonnegative Ricci curvature is studied. Under suitable volume conditions, the smooth solution will blow up in finite time no matter how small the initial data is, which follows from a new weight function and ODE inequalities. Moreover, the upper-bound of the lifespan can be estimated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-04T13:16:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01"
    ],
    "keywords": [
      "nonnegative ricci curvature",
      "fractional schrödinger equations",
      "power type nonlinearity",
      "ode inequalities",
      "cauchys problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}