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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Scattering for $ \dot{\mathrm{H}}^{1/2}$ 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 $ 1/2$ 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: http://dx.doi.org/10.1090/S0002-9947-09-04722-9
PII: S 0002-9947(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.