Advances in Differential Equations

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

Casey Rodriguez

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

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

Dates
First available in Project Euclid: 9 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1457536499

Mathematical Reviews number (MathSciNet)
MR3473583

Zentralblatt MATH identifier
1348.35033

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

Citation

Rodriguez, Casey. Profiles for the radial focusing energy-critical wave equation in odd dimensions. Adv. Differential Equations 21 (2016), no. 5/6, 505--570. https://projecteuclid.org/euclid.ade/1457536499.


Export citation