@article{22086,
  abstract     = {We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrödinger equations in dimensions n ≥ 3, for solutions which have large, but finite, energy and large, but finite, Strichartz norms. For dimensions n ≤ 6, this theory is a standard extension of the small data well-posedness theory based on iteration in Strichartz spaces. However, in dimensions n > 6 there is an obstruction to this approach because of the subquadratic nature of the nonlinearity (which makes the derivative of the nonlinearity non-Lipschitz). We resolve this by iterating in exotic Strichartz spaces instead. The theory developed here will be applied in a subsequent paper of the second author, [21], to establish global well-posedness and scattering for the defocusing energy-critical equation for large energy data.},
  author       = {Tao, Terence and Visan, Monica},
  issn         = {1550-6150},
  journal      = {Electronic Journal of Differential Equations},
  number       = {118},
  pages        = {1--28},
  publisher    = {Texas State University},
  title        = {{Stability of energy-critical nonlinear Schrodinger equations in high dimensions}},
  volume       = {2005},
  year         = {2005},
}