{
  "id": "math/0409585",
  "version": "v1",
  "published": "2004-09-29T18:45:26.000Z",
  "updated": "2004-09-29T18:45:26.000Z",
  "title": "Ground state mass concentration in the L^2-critical nonlinear Schrodinger equation below H^1",
  "authors": [
    "Jim Colliander",
    "Sarah Raynor",
    "Catherine Sulem",
    "J. Douglas Wright"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider finite time blowup solutions of the $L^2$-critical cubic focusing nonlinear Schr\\\"odinger equation on $\\R^2$. Such functions, when in $H^1$, are known to concentrate a fixed $L^2$-mass (the mass of the ground state) at the point of blowup. Blowup solutions from initial data that is only in $L^2$ are known to concentrate at least a small amount of mass. In this paper we consider the intermediate case of blowup solutions from initial data in $H^s$, with $1 > s > s_Q$, where $s_Q \\le \\sQ$. Our main result is that such solutions, when radially symmetric, concentrate at least the mass of the ground state at the origin at blowup time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-29T18:45:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35B33"
    ],
    "keywords": [
      "ground state mass concentration",
      "nonlinear schrodinger equation",
      "finite time blowup solutions",
      "initial data",
      "concentrate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9585C"
    }
  }
}