Soliton resolution for energy-critical equivariant wave maps (in-person talk)

Soliton resolution for energy-critical equivariant wave maps (in-person talk)

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Andrew Lawrie, MIT (NOTE SPECIAL DAY/TIME)
Fine Hall 314

Zoom link: https://princeton.zoom.us/j/92147928280?pwd=aGJ4VStpUTI2RWh1Y2FqTjlGQnZGQT09

I will present a joint work with Jacek Jendrej (CRNS, Sorbonne Paris Nord) on equivariant wave maps with values in a sphere. We prove that every finite energy solution 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 the resolution holds continuously-in-time via a “no-return” analysis based on the virial identity. The proof combines a modulation analysis of solutions near a multi-soliton configuration with concentration compactness techniques.