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

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.