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Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in $\R^{1+4}$

E. Ryckman·M. Visan
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Abstract

We obtain global well-posedness, scattering, uniform regularity, and global $L^6_{t,x}$ spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in $\R\times\R^4$. Our arguments closely follow those of Colliander-Keel-Staffilani-Takaoka-Tao, though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the $L^6_{t,x}$-norm.

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E. Ryckman, M. Visan. 2006-03-05. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in $\R^{1+4}$. https://arxiv.org/abs/math/0501462

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