Séminaire Analyse Numérique et EDP
Soliton resolution for the energy-critical wave maps equation in the equivariant case
Feb. 2023
Feb. 2023
Intervenant : Jacek Jendrej
Institution : Université Sorbonne Paris-Nord
Heure : 14h00 - 15h00
Lieu : 3L8

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.

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