Dynamics for the energy critical nonlinear wave equation in high dimensions
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- by Dong Li and Xiaoyi Zhang PDF
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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 $W$.References
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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
- MR Author ID: 714906
- Email: zh.xiaoyi@gmail.com
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 1137-1160
- MSC (2010): Primary 35Q55, 35L05, 35L71
- DOI: https://doi.org/10.1090/S0002-9947-2010-04999-2
- MathSciNet review: 2737260