Global well-posedness and scattering for the energy-critical Schrödinger equation in ℝ<sup>3</sup>
Global well-posedness and scattering for the energy-critical Schrödinger equation in ℝ<sup>3</sup>
We obtain global well-posedness, scattering, and global L 10 t,x spacetime bounds for energy-class solutions to the quintic defocusing Schrödinger equation in R 1+3 , which is energy-critical.In particular, this establishes global existence of classical solutions.Our work extends the results of Bourgain [4] and Grillakis [20], which handled the radial …