Scattering for bounded solutions to the cubic, defocusing NLS in 3 dimensions

Authors:
Carlos E. Kenig and Frank Merle

Journal:
Trans. Amer. Math. Soc. **362** (2010), 1937-1962

MSC (2010):
Primary 35Q55

Published electronically:
November 18, 2009

MathSciNet review:
2574882

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Abstract: We show that if a solution of the defocusing cubic NLS in 3d remains bounded in the homogeneous Sobolev norm of order in its maximal interval of existence, then the interval is infinite and the solution scatters. No radial assumption is made.

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Additional Information

**Carlos E. Kenig**

Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637

Email:
cek@math.uchicago.edu

**Frank Merle**

Affiliation:
Departement de Mathematiques, Universite de Cergy–Pontoise, Pontoise 95302 Cergy–Pontoise, France

Email:
Frank.Merle@math.u-cergy.fr

DOI:
https://doi.org/10.1090/S0002-9947-09-04722-9

Received by editor(s):
September 20, 2007

Published electronically:
November 18, 2009

Additional Notes:
The first author was supported in part by NSF

The second author was supported in part by CNRS. Part of this research was carried out during visits of the second author to the University of Chicago and IHES. This research was also supported in part by ANR ONDE NONLIN

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.