{
  "id": "1501.01414",
  "version": "v1",
  "published": "2015-01-07T09:39:06.000Z",
  "updated": "2015-01-07T09:39:06.000Z",
  "title": "On Fractional Schrodinger Equations in sobolev spaces",
  "authors": [
    "Younghun Hong",
    "Yannick Sire"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\sigma\\in(0,1)$ with $\\sigma\\neq\\frac{1}{2}$. We investigate the fractional nonlinear Schr\\\"odinger equation in $\\mathbb R^d$: $$i\\partial_tu+(-\\Delta)^\\sigma u+\\mu|u|^{p-1}u=0,\\, u(0)=u_0\\in H^s,$$ where $(-\\Delta)^\\sigma$ is the Fourier multiplier of symbol $|\\xi|^{2\\sigma}$, and $\\mu=\\pm 1$. This model has been introduced by Laskin in quantum physics \\cite{laskin}. We establish local well-posedness and ill-posedness in Sobolev spaces for power-type nonlinearities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-07T09:39:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional schrodinger equations",
      "sobolev spaces",
      "fourier multiplier",
      "power-type nonlinearities",
      "quantum physics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150101414H"
    }
  }
}