The APDE seminar on Monday, 10/11, will be given by Jacek Jendrej (Université Sorbonne Paris Nord) online via Zoom from 9.10am to 10.00am PST (note the time change). To participate, email Sung-Jin Oh (email@example.com)
Title: Soliton resolution for energy-critical equivariant wave maps
Abstract: We consider wave maps R^(1+2) -> S^2, under the assumption of equivariant symmetry. We prove that every solution of finite energy resolves, as time passes, into a superposition of harmonic maps (solitons) and radiation. It was proved in works of Côte, and Jia and Kenig, that such a decomposition holds along a sequence of times. We show that the resolution holds continuously in time via a “no-return lemma” based on the virial identity. The proof combines a modulation analysis of solutions near a multi-soliton configuration with the concentration-compactness method. Joint work with Andrew Lawrie from MIT.