Cambridge Journal of Mathematics

Volume 1 (2013)

Number 1

Classification of the radial solutions of the focusing, energy-critical wave equation

Pages: 75 – 144



Thomas Duyckaerts (Université Paris 13, LAGA, Villetaneuse, France)

Carlos Kenig (Department of Mathematics, University of Chicago, Chicago, Illinois, U.S.A.)

Frank Merle (Département de Mathématiques, Université de Cergy-Pontoise, France)


In this paper, we describe the asymptotic behaviour of globally defined solutions and of bounded solutions blowing up in finite time of the radial energy-critical focusing non-linear wave equation in three-space dimension.


wave equation, global well-posedness, blowup, asymptotic behaviour, soliton resolution

2010 Mathematics Subject Classification

Primary 35L05. Secondary 35B40, 35B44, 35L71.

Published 6 June 2013