---
res:
  bibo_abstract:
  - "We consider the focusing energy-critical nonlinear Schr\\\"odinger equation \r\n$iu_t+\\Delta
    u = - |u|^{4\\over{d-2}}u$ in dimensions $d\\geq 5$. We prove \r\nthat if a maximal-lifespan
    solution $u\\colon \\ I\\times {\\Bbb R}^d\\to {\\Bbb C}$ obeys $\\sup_{t\\in
    I}\\|\\nabla u(t)\\|_2<\\|\\nabla W\\|_2$, then it is \r\nglobal and scatters
    both forward and backward in time. Here $W$ denotes \r\nthe ground state, which
    is a stationary solution of the equation. In \r\nparticular, if a solution has
    both energy and kinetic energy less than \r\nthose of the ground state $W$ at
    some point in time, then the solution is \r\nglobal and scatters. We also show
    that any solution that blows up with \r\nbounded kinetic energy must concentrate
    at least the kinetic energy of the \r\nground state. Similar results were obtained
    by Kenig and Merle for \r\nspherically symmetric initial data and dimensions $d=3,4,5$.\r\n</jats:p>@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Rowan
      foaf_name: Killip, Rowan
      foaf_surname: Killip
  - foaf_Person:
      foaf_givenName: Monica
      foaf_name: Visan, Monica
      foaf_surname: Visan
      foaf_workInfoHomepage: http://www.librecat.org/personId=056daca0-b8d1-11f0-964f-f91054abf8ca
  bibo_doi: 10.1353/ajm.0.0107
  bibo_issue: '2'
  bibo_volume: 132
  dct_date: 2010^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1080-6377
  dct_language: eng
  dct_publisher: Johns Hopkins University Press@
  dct_title: The focusing energy-critical nonlinear Schrödinger equation in dimensions
    five and higher@
...