The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions

Abstract

We obtain global well-posedness, scattering, and global $L_{t,x}^{2(n+2)/(n-2)}$ space-time bounds for energy-space solutions to the energy-critical nonlinear Schrödinger (NLS) equation in ${\mathbb{R}}_t\times {\mathbb{R}}_x^n$, $n\ge 5$