Repository logo

Infoscience

  • English
  • French
Log In
Logo EPFL, École polytechnique fédérale de Lausanne

Infoscience

  • English
  • French
Log In
  1. Home
  2. Academic and Research Output
  3. Preprints and Working Papers
  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.

  • Files
  • Details
  • Metrics
Loading...
Thumbnail Image
Name

TwoBubbleBlowup-Jan2025_1.pdf

Type

Main Document

Version

Submitted version (Preprint)

Access type

openaccess

License Condition

CC BY

Size

343.11 KB

Format

Adobe PDF

Checksum (MD5)

75e29ae0368ca42c4d7cdfc9224f89c3

Logo EPFL, École polytechnique fédérale de Lausanne
  • Contact
  • infoscience@epfl.ch

  • Follow us on Facebook
  • Follow us on Instagram
  • Follow us on LinkedIn
  • Follow us on X
  • Follow us on Youtube
AccessibilityLegal noticePrivacy policyCookie settingsEnd User AgreementGet helpFeedback

Infoscience is a service managed and provided by the Library and IT Services of EPFL. © EPFL, tous droits réservés