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

 

Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation


Authors: Slim Ibrahim, Nader Masmoudi and Kenji Nakanishi
Journal: Trans. Amer. Math. Soc. 366 (2014), 5653-5669
MSC (2010): Primary 35L70, 35B40, 35B44, 47J30
Published electronically: May 20, 2014
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Abstract: We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy extends to the threshold energy in the case of mass-shift for the critical nonlinear Klein-Gordon equation.


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Additional Information

Slim Ibrahim
Affiliation: Department of Mathematics and Statistics, University of Victoria, PO Box 3060 STN CSC, Victoria, British Columbia, Canada V8P 5C3
Email: ibrahim@math.uvic.ca

Nader Masmoudi
Affiliation: The Courant Institute for Mathematical Sciences, New York University, New York, New York 10012
Email: masmoudi@courant.nyu.edu

Kenji Nakanishi
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Email: n-kenji@math.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05852-2
PII: S 0002-9947(2014)05852-2
Received by editor(s): October 7, 2011
Received by editor(s) in revised form: April 10, 2012
Published electronically: May 20, 2014
Additional Notes: The first author was partially supported by NSERC# 371637-2009 grant and a start up fund from the University of Victoria
The second author was partially supported by an NSF Grant DMS-0703145
Article copyright: © Copyright 2014 American Mathematical Society