Abstract

abstract:

Consider the defocusing quintic nonlinear Schr\"{o}dinger equation on ${\bf R}^3$ with initial data in the energy space. This problem is ``energy-critical'' in view of a certain scale-invariance, which is a main source of difficulty in the analysis of this equation. It is a nontrivial fact that all finite-energy solutions scatter to linear solutions. We show that this remains true under small compact deformations of the Euclidean metric. Our main new ingredient is a long-time microlocal weak dispersive estimate that accounts for the refocusing of geodesics.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 981-1035
Launched on MUSE
2019-07-24
Open Access
No
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