Scattering below the ground state for the 2$d$ radial nonlinear Schrödinger equation
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- by Anudeep Kumar Arora, Benjamin Dodson and Jason Murphy PDF
- Proc. Amer. Math. Soc. 148 (2020), 1653-1663 Request permission
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.References
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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
- MR Author ID: 891326
- Email: bdodson4@jhu.edu
- Jason Murphy
- Affiliation: Department of Mathematics & Statistics, Missouri University of Science & Technology, Rolla, Missouri 65409
- MR Author ID: 1034475
- Email: jason.murphy@mst.edu
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1653-1663
- MSC (2010): Primary 35Q55
- DOI: https://doi.org/10.1090/proc/14824
- MathSciNet review: 4069202