École polytechnique – Centre de Mathématiques Laurent Schwartz

10h30 – Arthur Touati (CMLS)

"Global existence for high-frequency solutions to a semi-linear wave equation with a null structure"

In this talk (given in french but with slides in english) I will present a work on high-frequency solutions to non-linear wave equations.
This topic is particularly interesting in  general relativity, for instance in the context of the Burnett's conjecture.
I will explain why a semi-linear wave equation with a null structure is a nice toy model for the Einstein equations, and then adress the question of global existence for high-frequency solutions. To this end, I will construct an ansatz which captures the self-interaction of the waves and then derive a hierarchy of equations for the different terms. Finally I will show how one can prove global existence for this hierarchy, especially highlighting the interaction between the high-frequency features and the usual vector field method.

Le groupe de travail aura lieu à l'adresse suivante :

https://ecolepolytechnique.zoom.us/j/88423623816?pwd=S0NxRGE5c2JOVFhPOWR4YXgrYlEwQT09

ID de réunion : 884 2362 3816

Code secret : 853794