Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data

@inproceedings{Tao2005GlobalWA,
  title={Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schr{\"o}dinger equation for radial data},
  author={Terence Tao},
  year={2005}
}
In any dimension n ≥ 3, we show that spherically symmetric bounded energy solutions of the defocusing energy-critical nonlinear Schrödinger equation iut + ∆u = |u| 4 n−2 u in R × Rn exist globally and scatter to free solutions; this generalizes the three and four-dimensional results of Bourgain, 1999a and 1999b, and Grillakis, 2000. Furthermore we have… CONTINUE READING