Threshold for blowup for the supercritical cubic wave equation

Irfan Glogić, Maciej Maliborski, Birgit Schörkhuber

Published 2019-05-31Version 1

In this paper, we discuss singularity formation for the focusing cubic wave equation in the energy supercritical regime. For this equation an $\textit{explicit}$ nontrivial self-similar blowup solution was recently found by the first and third author in \cite{GlogicSchoerkhuber}. In the seven dimensional case it was proven to be stable along a co-dimension one manifold of initial data. Here, we provide numerical evidence that this solution is in fact a critical solution at the threshold between finite-time blowup and dispersion. Furthermore, we discuss the spectral problem arising in the stability analysis in general dimensions $d \geq 5$.