Advances in Differential Equations

Profiles for the radial focusing energy-critical wave equation in odd dimensions

Casey Rodriguez

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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.

Article information

Adv. Differential Equations, Volume 21, Number 5/6 (2016), 505-570.

First available in Project Euclid: 9 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B40: Asymptotic behavior of solutions 35L71: Semilinear second-order hyperbolic equations


Rodriguez, Casey. Profiles for the radial focusing energy-critical wave equation in odd dimensions. Adv. Differential Equations 21 (2016), no. 5/6, 505--570.

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