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Scattering below the ground state for the 2$ d$ radial nonlinear Schrödinger equation


Authors: Anudeep Kumar Arora, Benjamin Dodson and Jason Murphy
Journal: Proc. Amer. Math. Soc. 148 (2020), 1653-1663
MSC (2010): Primary 35Q55
DOI: https://doi.org/10.1090/proc/14824
Published electronically: December 6, 2019
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Abstract: We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear Schrödinger equation in two space dimensions. We present a simple new proof that treats the case of radial initial data. The key ingredient is a localized virial/Morawetz estimate; the radial assumption aids in controlling the error terms resulting from the spatial localization.


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Additional Information

Anudeep Kumar Arora
Affiliation: Department of Mathematics & Statistics, Florida International University, Miami, Florida 33199
Email: ana001@fiu.edu

Benjamin Dodson
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email: bdodson4@jhu.edu

Jason Murphy
Affiliation: Department of Mathematics & Statistics, Missouri University of Science & Technology, Rolla, Missouri 65409
Email: jason.murphy@mst.edu

DOI: https://doi.org/10.1090/proc/14824
Received by editor(s): June 2, 2019
Received by editor(s) in revised form: July 24, 2019, and August 21, 2019
Published electronically: December 6, 2019
Additional Notes: The second author was supported by NSF DMS-1764358 and completed part of this work while a von Neumann fellow at the Institute for Advanced Study
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society