A note on concentration for blowup solutions to supercritical Schrödinger equations
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Abstract:
We study the blowup dynamics of solutions to the $L^2$-supercritical nonlinear Schrödinger equation and prove that the blowup solution with bounded $\dot H^{s_c}$ norm must concentrate at least a fixed amount of the $\dot H^{s_c}$ norm and, also, its $L^{p_c}$ norm must concentrate at least a fixed $L^{p_c}$ norm. We show these properties without any further symmetry assumptions on the solution and partly generalize the results obtained in papers of Holmer and Roudenko and of Zhu, which only deal with the radially symmetric case. Our proof is based on the profile decomposition theorems.References
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Additional Information
- Qing Guo
- Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- Address at time of publication: College of Science, Minzu University of China, Beijing 100081, People’s Republic of China
- Email: guoqing@amss.ac.cn
- Received by editor(s): May 3, 2011
- Received by editor(s) in revised form: November 8, 2011, and January 8, 2012
- Published electronically: August 30, 2013
- Communicated by: James E. Colliander
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 4215-4227
- MSC (2010): Primary 35Q55, 35A15; Secondary 35B30
- DOI: https://doi.org/10.1090/S0002-9939-2013-11735-1
- MathSciNet review: 3105865