## Profiles for the Radial Focusing 4d Energy-Critical Wave Equation

##### Author(s)

Côte, R.; Schlag, W.; Kenig, C. E.; Lawrie, Andrew W
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Show full item record##### Abstract

Consider a finite energy radial solution to the focusing energy critical semilinear wave equation in 1 + 4 dimensions. Assume that this solution exhibits type-II behavior, by which we mean that the critical Sobolev norm of the evolution stays bounded on the maximal interval of existence. We prove that along a sequence of times tending to the maximal forward time of existence, the solution decomposes 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 that the critical norm of the evolution localized to the light cone (the forward light cone in the case of global solutions and the backwards cone in the case of finite time blow-up) is less than 2 times the critical norm of the ground state solution W, then the decomposition holds without a restriction to a subsequence.

##### Date issued

2017-12##### Department

Massachusetts Institute of Technology. Department of Mathematics##### Journal

Communications in Mathematical Physics

##### Publisher

Springer Berlin Heidelberg

##### Citation

Côte, R., et al. “Profiles for the Radial Focusing 4d Energy-Critical Wave Equation.” Communications in Mathematical Physics, vol. 357, no. 3, Feb. 2018, pp. 943–1008.

Version: Author's final manuscript

##### ISSN

0010-3616

1432-0916