Wednesday, April 30, 2025 - 16:15 in B2-238
On stable self-similar blowup for nonlinear wave equations beyond light cones
A talk in the Oberseminar Analysis series by
Matthias Ostermann
| Abstract: |
Exciting topics among the dynamics of nonlinear evolution equa-
tions are the occurrence and stability of finite time blowup solutions.
In fact, the wave maps equation, Yang-Mills equation, and focusing
semilinear wave equation all admit self-similar blowup solutions in
closed form. In this talk, I will present a comprehensive stability the-
ory for self-similar blowup solutions of these nonlinear wave equations,
which was obtained recently in my PhD thesis. The underlying analysis
is based on coordinate systems that are adapted to self-similarity and
compatible with the wave evolution. This allows to study the wave flow
near self-similar blowup solutions in spacetime regions that reach from
the backward light cone towards the future light cone of the respective
singularity.
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