Soliton resolution for the energy-critical wave maps equation in the equivariant case

Nom de l'orateur
Jacek Jendrej
Etablissement de l'orateur
LAGA, Université Sorbonne Paris Nord
Date et heure de l'exposé
Lieu de l'exposé
Salle des séminaires

I will present a joint work with Andrew Lawrie (MIT) on the wave maps equation from the (1+2)-dimensional space to the 2-dimensional sphere, in the case of initial data having the equivariant symmetry. We prove that every solution of finite energy converges in large time to a superposition of harmonic maps (solitons) and radiation. It was proved by Côte, and Jia and Kenig, that such a decomposition is true for a sequence of times. Combining the study of the dynamics of multi-solitons by the modulation technique with the concentration-compactness method, we prove a "non-return lemma", which allows to improve the convergence for a sequence of times to convergence in continuous time.