##### Department of Mathematics,

University of California San Diego

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### Math 248 - Analysis Seminar

## Andrew W Lawrie

#### MIT

## The soliton resolution conjecture for equivariant wave maps

##### Abstract:

I will present joint work with Jacek Jendrej (CRNS, Sorbonne Paris Nord) on equivariant wave maps with values in the two-sphere. We prove that every finite energy equivariant wave map resolves, as time passes, into a superposition of decoupled harmonic maps and radiation, settling the soliton resolution conjecture for this equation. 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” lemma based on the virial identity. The proof combines a collision analysis of solutions near a multi-soliton configuration with concentration compactness techniques. As a byproduct of our analysis we also prove that there are no elastic collisions between pure multi-solitons.

### February 1, 2022

### 11:00 AM

https://ucsd.zoom.us/j/

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