Threshold for blowup for the supercritical cubic wave equation

Author(s)
Irfan Glogić, Maciej Maliborski, Birgit Schörkhuber
Abstract

We consider the focusing cubic wave equation in the energy supercritical case, i.e. in dimensions . For this model an explicit nontrivial self-similar blowup solution was recently found by the first and third author in Glogić and Schörkhuber (2018 (arXiv:1810.07681)). Furthermore, the solution is proven to be co-dimension one stable in d  =  7. In this paper, we study the equation from a numerical point of view. For d  =  5 and d  =  7 in the radial case, we provide evidence that this solution is at the threshold between generic ODE blowup and dispersion. In addition, we investigate the spectral problem that underlies the stability analysis and compute the spectrum in general supercritical dimensions.

Organisation(s)
Department of Mathematics, Gravitational Physics
External organisation(s)
Karlsruher Institut für Technologie
Journal
Nonlinearity
Volume
33
Pages
2143-2158
No. of pages
16
ISSN
0951-7715
DOI
https://doi.org/10.1088/1361-6544/ab6f4d
Publication date
03-2020
Peer reviewed
Yes
Austrian Fields of Science 2012
101002 Analysis, 103019 Mathematical physics
Keywords
ASJC Scopus subject areas
Physics and Astronomy(all), Applied Mathematics, Statistical and Nonlinear Physics, Mathematical Physics
Portal url
https://ucris.univie.ac.at/portal/en/publications/threshold-for-blowup-for-the-supercritical-cubic-wave-equation(58457346-6cc0-4ec3-9f79-a5b275783c39).html