---
res:
  bibo_abstract:
  - "We undertake a comprehensive study of the nonlinear Schrödinger equation (mathematical
    formular) where u(t, x) is a complex-valued function in spacetime R, xRn/x, λ1
    and λ2 are nonzero real constants, and (mathematical formular). We address questions
    related to local and global well-posedness, finite time blowup, and asymptotic
    behaviour. Scattering is considered both in the energy space H^1(ℝ n ) and in
    the pseudoconformal space Σ := {f ∈ H^1(ℝ^n); xf ∈ L^2(ℝ^n)}. Of particular interest
    is the case when both nonlinearities are defocusing and correspond to the L2/x-critical,
    respectively H1/x-critical NLS, that is, λ1, λ2 > 0 and (mathematical formular)
    . The results at the endpoint p1= 4/n are conditional on a conjectured global
    existence and spacetime estimate for the L2/x-critical nonlinear Schrödinger equation,
    which has been verified in dimensions n ≥ 2 for radial data in Tao et al. (Tao
    et al. to appear a,b) and Killip et al. (preprint).\r\nAs an off-shoot of our
    analysis, we also obtain a new, simpler proof of scattering in H1/x for solutions
    to the nonlinear Schrödinger equation (mathematical formular) with 4/n < p < 4/n-2,
    which was first obtained by Ginibre and Velo (Citation1985).@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Terence
      foaf_name: Tao, Terence
      foaf_surname: Tao
  - foaf_Person:
      foaf_givenName: Monica
      foaf_name: Visan, Monica
      foaf_surname: Visan
      foaf_workInfoHomepage: http://www.librecat.org/personId=056daca0-b8d1-11f0-964f-f91054abf8ca
  - foaf_Person:
      foaf_givenName: Xiaoyi
      foaf_name: Zhang, Xiaoyi
      foaf_surname: Zhang
  bibo_doi: 10.1080/03605300701588805
  bibo_issue: '8'
  bibo_volume: 32
  dct_date: 2007^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0360-5302
  - http://id.crossref.org/issn/1532-4133
  dct_language: eng
  dct_publisher: Informa UK Limited@
  dct_subject:
  - Energy-critical
  - Mass-critical
  - Nonlinear Schrödinger equation
  - Wellposedness
  dct_title: The nonlinear Schrödinger equation with combined power-type nonlinearities@
...