Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4

E. Ryckman, Monica Vişan

Type: Article

Publication Date: 2007-02-01

Citations: 284

DOI: https://doi.org/10.1353/ajm.2007.0004

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 âÃâ4. 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.

Locations

American Journal of Mathematics - View
arXiv (Cornell University) - View - PDF

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