Profiles of bounded radial solutions of the focusing, energy-critical wave equation

Details Profiles of bounded radial solutions of the focusing, energy-critical wave equation Profiles of bounded radial solutions of the focusing, energy-critical wave equation

2012-01-24

arxiv.org/abs/1201.4986v1

Mathematics

Analysis of PDEs

To appear in GAFA

Scientific paper

In this paper we consider global and non-global bounded radial solutions of the focusing energy-critical wave equation in space dimension 3. We show that any of these solutions decouples, along a sequence of times that goes to the maximal time of existence, as a sum of modulated stationary solutions, a free radiation term and a term going to 0 in the energy space. In the case where there is only one stationary profile, we show that this expansion holds asymptotically without restriction to a subsequence.

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