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Dynamics at the threshold for blowup for supercritical wave equations outside a ball*

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Published 26 May 2020 • © 2020 IOP Publishing Ltd & London Mathematical Society
, , Citation Piotr Bizoń and Maciej Maliborski 2020 Nonlinearity 33 3195 DOI 10.1088/1361-6544/ab8352

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Author e-mails

bizon@th.if.uj.edu.pl

maciej.maliborski@univie.ac.at

Author affiliations

1 Institute of Theoretical Physics, Jagiellonian University, Kraków, Poland

2 Gravitational Physics, Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

Author notes

3 Author to whom any correspondence should be addressed.

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Dates

  1. Received 5 September 2019
  2. Revised 22 March 2020
  3. Accepted 25 March 2020
  4. Published

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0951-7715/33/7/3195

Abstract

We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a codimension-one stable manifold of the unique static solution with exactly one unstable direction. We analyse in detail the convergence to this critical solution for initial data fine-tuned to the threshold.

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Footnotes

  • * 

    This research was supported by the Polish National Science Centre Grant No. 2017/26/A/ST2/00530. Computations have been performed on Minerva cluster of the Max-Planck Institute for Gravitational Physics.

10.1088/1361-6544/ab8352