Abstract

We obtain global well-posedness, scattering, uniform regularity, and global L6t,x spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in ℝ×ℝ4. Our arguments closely follow those of Colliander, Keel, et al., though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the L6t,x-norm.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1-60
Launched on MUSE
2007-02-16
Open Access
No
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