Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions

Abstract

We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation ${\mathrm{iu}}_t+\Delta u=|u{|}^{4/n}u$ for large, spherically symmetric, $L_x^2({\mathbb{R}}^n)$ initial data in dimensions $n\ge 3$. After using the concentration-compactness reductions in [32] to reduce to eliminating blow-up solutions that are almost periodic modulo scaling, we obtain a frequency-localized Morawetz estimate and exclude a mass evacuation scenario (somewhat analogously to [10], [23], [36]) in order to conclude the argument