Matthias Ostermann - Stable self-similar blowup for nonlinear wave equations beyond light cones

This talk was part of the Thematic Programme on "Nonlinear Waves and Relativity" held at the ESI April 29 -- June 21, 2024.
We consider the corotational wave maps equation and Yang-Mills equation in all energy-supercritical dimensions. These are exemplary geometric wave equations with an explicit self-similar blowup solution. In fact, both solutions continue to exist even past the singularity. In this talk, we present new stability results for these blowup solutions in spacetime regions that extend beyond the backward light cone of the singularity towards its future light cone. The underlying setting is based on coordinate systems that are adapted to self-similarity and compatible with the wave evolution, thereby allowing to evolve the flow near the self-similar blowup in such spacetime regions.