On generic blowup for the supercritical wave maps equation
A talk in the Oberseminar Analysis series by
Irfan Glogic
| Abstract: | We consider wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere. Numerical simulations of this model indicate that in the energy supercritical case, $d \geq 3$, generic large data lead to finite time blowup via an explicitly known self-similar solution. In the effort of rigorously proving these observations, many works have been produced over the last decade, starting with the pioneering works of Aichelburg-Donninger-Sch\"orkhuber. In this talk, we outline a novel general framework for the analysis of spatially global stability of self-similar solutions to semilinear wave equations. We then implement this scheme in the aforementioned context of wave maps, thereby obtaining the first nonlinear stability result that is global-in-space. At the end, we discuss further open problems as well as the new mathematical challenges that our approach generates. Within the CRC this talk is associated to the project(s): A1 |