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

Abstract

We consider the equivariant wave maps equation ${\mathbb{R}}^{1+2}\to {\mathbb{S}}^2$, in all equivariance classes $k\in \mathbb{N}$. We prove that every finite energy solution resolves, continuously in time, into a superposition of asymptotically decoupling harmonic maps and free radiation.

arXiv comment78 pages; in the new version we have included Proposition 1.6 (and its proof in Section 5.4), which shows that the only solutions that are pure multi-bubbles in both time directions are the stationary solutions