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

 

Dynamics for the energy critical nonlinear wave equation in high dimensions


Authors: Dong Li and Xiaoyi Zhang
Journal: Trans. Amer. Math. Soc. 363 (2011), 1137-1160
MSC (2010): Primary 35Q55, 35L05, 35L71
Published electronically: October 19, 2010
MathSciNet review: 2737260
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Abstract: T. Duyckaerts and F. Merle (2008) studied the variational structure near the ground state solution $ W$ of the energy critical wave equation and classified the solutions with the threshold energy $ E(W,0)$ in dimensions $ d=3,4,5$. In this paper, we extend the results to all dimensions $ d\ge 6$. The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of $ W$.


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Additional Information

Dong Li
Affiliation: Department of Mathematics, University of Iowa, Maclean Hall, Iowa City, Iowa 52242
Email: mpdongLi@gmail.com

Xiaoyi Zhang
Affiliation: Department of Mathematics, University of Iowa, Maclean Hall, Iowa City, Iowa 52242 – and – Chinese Academy of Sciences, Beijing, People’s Republic of China
Email: zh.xiaoyi@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-04999-2
PII: S 0002-9947(2010)04999-2
Keywords: Energy-critical wave equation, dynamical behavior, ground state
Received by editor(s): June 16, 2008
Published electronically: October 19, 2010
Additional Notes: The first and second authors were supported in part by the National Science Foundation under agreement No. DMS-0635607 and a start-up funding from the Mathematics Department of the University of Iowa. The second author was also supported by NSF grant No. 10601060 and project 973 in China
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.