# Two-bubble dynamics for threshold wave maps. November 13, 2017 - 3:00pm PDE and Analysis Seminar

### Speaker Information

(joint with Jacek Jendrej)

We consider energy-critical wave maps taking values in the 2-sphere. It is known that initial data of topological degree zero and energy less than twice that of the ground state harmonic map leads to a global solution that scatters in both time directions. In this talk we’ll consider data at the threshold energy. For any k-equivariant data with exactly twice the energy of the degree k equivariant harmonic map we prove that the solution is defined globally in time and either scatters in both time directions, or converges to a superposition of two harmonic maps in one time direction and scatters in the other time direction. In the latter case, we describe the asymptotic behavior of the scales of the two harmonic maps. The proof combines classical concentration-compactness techniques with a modulation analysis of interactions between two harmonic maps in the absence of excess radiation.