Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4

Source abstract

We obtain global well-posedness, scattering, uniform regularity, and global L6t,x spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in ℝ×ℝ4. Our arguments closely follow those of Colliander, Keel, et al., though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the L6t,x-norm.