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

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

Jendrej, Jacek
•
Krieger, Joachim  
January 14, 2025

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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Type
preprint
Author(s)
Jendrej, Jacek

Sorbonne Université

Krieger, Joachim  

EPFL

Date Issued

2025-01-14

Subjects

critical wave maps

•

blowup

•

bubble trees

Editorial or Peer reviewed

NON-REVIEWED

Written at

EPFL

EPFL units
PDE  
Available on Infoscience
January 20, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/243046
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