Global well-posedness and scattering for the 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 $i{u}_t+\Delta u=|u{|}^{4/n}u$ for large spherically symmetric $L_x^2({\mathbb{R}}^n)$ initial data in dimensions $n\ge 3$. After using the reductions in \cite{compact} to reduce to eliminating blowup solutions which are almost periodic modulo scaling, we obtain a frequency-localized Morawetz estimate and exclude a mass evacuation scenario (somewhat analogously to \cite{ckstt:gwp}, \cite{RV}, \cite{thesis:art}) in order to conclude the argument.

Contains updated references and related remarks

Cited by in corpus (1)

• Global regularity of wave maps III. Large energy from ${\mathbb{R}}^{1+2}$ to hyperbolic spaces