Publication

Concentric bubbles concentrating in finite time for the energy critical Wave Maps equation

2025

Abstract

We show that the energy critical Wave Maps equation from R 2+1 to S 2 and restricted to the co-rotational setting with co-rotation index k = 2 admits finite time blow up solutions of finite energy on (0, t 0] x R 2 , t 0 > 0, and concentrating two concentric bubble profiles at the frequency scales λ 1 (t) = e α(t) , α(t) ~ |log t|β+1 , as well as λ 2(t) = t-1 · |log t|β. The parameter β > 3/2 can be chosen arbitrarily. This shows that soliton resolution scenarios with finite time blow up and N = 2 collapsing profiles, i. e. bubble trees, do occur for this equation.

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2025

Abstract

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