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A new proof of scattering below the ground state for the 3d radial focusing cubic NLS


Authors: Benjamin Dodson and Jason Murphy
Journal: Proc. Amer. Math. Soc. 145 (2017), 4859-4867
MSC (2010): Primary 35Q55
DOI: https://doi.org/10.1090/proc/13678
Published electronically: June 5, 2017
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Abstract: We revisit the scattering result of Holmer and Roudenko (2008) on the radial focusing cubic NLS in three space dimensions. Using the radial Sobolev embedding and a virial/Morawetz estimate, we give a simple proof of scattering below the ground state that avoids the use of concentration compactness.


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Additional Information

Benjamin Dodson
Affiliation: Department of Mathematics, Johns Hopkins University, John Krieger Hall, 3400 North Charles Street, Baltimore, Maryland 21218
Email: bdodson4@jhu.edu

Jason Murphy
Affiliation: Departments of Mathematics, University of California Berkeley, 970 Evans Hall, Berkeley, California 94720
Email: murphy@math.berkeley.edu

DOI: https://doi.org/10.1090/proc/13678
Received by editor(s): December 13, 2016
Published electronically: June 5, 2017
Communicated by: Joachim Krieger
Article copyright: © Copyright 2017 American Mathematical Society