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

Seminar: 
Analysis
Event time: 
Thursday, October 27, 2022 - 4:15pm
Location: 
WLH 120
Speaker: 
Jacek Jendrej
Speaker affiliation: 
Université Sorbonne Paris Nord
Event description: 

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

Special note: 
Seminar talk is supported in part by the Mrs. Hepsa Ely Silliman Memorial Fund.