Continuous time soliton resolution for two-bubble equivariant wave maps

We consider the energy-critical wave maps equation R1+2 → S2 in the equivariant case. We prove that if a wave map decomposes, along a sequence of times, into a superposition of at most two rescaled harmonic maps (bubbles) and radiation, then such a decomposition holds for continuous time. We deduce, as a consequence of sequential soliton resolution results of Côte [5], and Jia and Kenig [25], that any topologically trivial equivariant wave map with energy less than four times the energy of the bubble asymptotically decomposes into (at most two) bubbles and radiation.