@article{22058,
  abstract     = {We consider the defocusing H˙ 1-critical nonlinear Schr¨odinger equation in all dimensions (n ≥ 3) with a quadratic potential V (x) = ± 1/2|x|^2. We show global well-posedness for radial initial data obeying ∇u0(x), xu0(x) ∈L^2. In view of the potential V , this is the natural energy space. In the repulsive case, we also prove scattering. We follow the approach pioneered by Bourgain and Tao in the case of no potential; indeed, we include a proof of their results that incorporates a
couple of simplifications discovered while treating the problem with quadratic potential.},
  author       = {Killip, Rowan and Visan, Monica and Zhang, Xiaoyi},
  issn         = {0360-5302},
  journal      = {Communications in Partial Differential Equations},
  number       = {12},
  pages        = {1531--1565},
  publisher    = {Informa UK Limited},
  title        = {{Energy-critical NLS with quadratic potentials}},
  doi          = {10.1080/03605300903328109},
  volume       = {34},
  year         = {2009},
}