Stable self-similar blowup in nonlinear wave equations

Self-similar singularity formation can be observed in many nonlinear PDEs ranging from dispersive equations to parabolic problems. In this talk, I outline an approach to study the nonlinear asymptotic stability of self-similar „ground states“ for semilinear wave equations. These solutions are conjectured to describe the generic blowup behavior of the respective models locally around the blowup point.
Several examples will be discussed including energy-supercritical focusing wave equations and corotational wave maps from Minkowski space into the three-sphere. For the latter, I also present recent progress concerning the investigation of the global blowup profile. The talk is based on joint work with Roland Donninger and Paweł Biernat (University of Bonn).