---
res:
  bibo_abstract:
  - "We consider the focusing energy-critical nonlinear Schrödinger equation iut +
    ∆u = −|u|\r\n4 d−2 u in dimensions d ≥ 5. We prove that if a maximal-lifespan
    solution u : I × Rd → C obeys supt∈I k∇u(t)k2 < k∇Wk2, then it is global and scatters
    both forward and backward in time. Here W denotes the ground state, which is a
    stationary solution of the equation. In\r\nparticular, if a solution has both
    energy and kinetic energy less than those\r\nof the ground state W at some point
    in time, then the solution is global and\r\nscatters. We also show that any solution
    that blows up with bounded kinetic\r\nenergy must concentrate at least the kinetic
    energy of the ground state. Similar\r\nresults were obtained by Kenig and Merle
    in [17, 18] for spherically symmetric\r\ninitial data and dimensions d = 3, 4,
    5.@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/0002-9327
  - 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@
...