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May/June 2016 Profiles for the radial focusing energy-critical wave equation in odd dimensions
Casey Rodriguez
Adv. Differential Equations 21(5/6): 505-570 (May/June 2016).

Abstract

In this paper, we consider global and non-global radial solutions of the focusing energy--critical wave equation on $\mathbb{R} \times \mathbb{R}^N$ where $N \geq 5$ is odd. We prove that if the solution remains bounded in the energy space as you approach the maximal forward time of existence, then along a sequence of times converging to the maximal forward time of existence, the solution decouples into a sum of dynamically rescaled solitons, a free radiation term, and an error tending to zero in the energy space. If, in addition, we assume a bound on the evolution that rules out the formation of multiple solitons, then this decoupling holds for all times approaching the maximal forward time of existence.

Citation

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Casey Rodriguez. "Profiles for the radial focusing energy-critical wave equation in odd dimensions." Adv. Differential Equations 21 (5/6) 505 - 570, May/June 2016.

Information

Published: May/June 2016
First available in Project Euclid: 9 March 2016

zbMATH: 1348.35033
MathSciNet: MR3473583

Subjects:
Primary: 35B40 , 35L71

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 5/6 • May/June 2016
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