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Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data (2004)
| Venue: | J. MATH |
| Citations: | 48 - 8 self |
BibTeX
@ARTICLE{Tao04globalwell-posedness,
author = {Terence Tao},
title = {Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data},
journal = {J. MATH},
year = {2004}
}
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Abstract
In any dimension n ≥ 3, we show that spherically symmetric bounded energy solutions of the defocusing energy-critical non-linear Schrödinger equation iut+∆u = |u | 4 n−2 u in R×Rn exist globally and scatter to free solutions; this generalizes the three and four dimensional results of Bourgain [1], [2] and Grillakis [11]. Furthermore we have bounds on various spacetime norms of the solution which are of exponential type in the energy, which improves on the tower-type bounds of Bourgain. In higher dimensions n ≥ 6 some new technical difficulties arise because of the very low power of the non-linearity.
