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

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

Terence Tao, Monica Visan and Xiaoyi Zhang
Duke mathematical journal, Vol.140(1), pp.165-202
10/01/2007
DOI: 10.1215/S0012-7094-07-14015-8

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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 + Δ u = | u | 4 / n u for large, spherically symmetric, L x 2 ( R n ) initial data in dimensions n ≥ 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
NLS-like equations (nonlinear Schrödinger) [See also 37K10]

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