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

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

2006-09-25

arxiv.org/abs/math/0609692v2

Mathematics

Analysis of PDEs

Contains updated references and related remarks

Scientific paper

We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schr\"odinger equation $iu_t + \Delta u = |u|^{4/n} u$ for large spherically symmetric $L^2_x(\R^n)$ initial data in dimensions $n\geq 3$. 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.

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