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

Terence Tao·Monica Visan·Xiaoyi Zhang
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Abstract

We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation $iu_t + Δu = |u|^{4/n} u$ 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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Terence Tao, Monica Visan, Xiaoyi Zhang. 2006-10-16. Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in high dimensions. https://arxiv.org/abs/math/0609692

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