Dispersive estimates for non-linear waves in mathematical General Relativity

Speaker：

Sari Ghanem (BIMSA)

Time：

Wed., 11:00-12:30 & 14:00-15:30

2025 Spring Semester

(from Feb. 19, 2025)

Venue：

A513, Shuangqing Complex Building A

Description：

This course introduces the tools of analysis for proving dispersive estimates for solutions of non-linear wave equations arising in General Relativity from the point of view of analysis and partial differential equations. The course material builds on one hand, on a previous course that I gave in the Spring 2024 on the Cauchy problem in mathematical General Relativity, and on the other hand, on a previous course that I gave in the Fall 2024 on non-linear wave equations in General Relativity. The goal of this course is to show a method to obtain dispersive estimates for solutions of tensorial coupled non-linear hyperbolic partial differential equations, provided that one exploits the non-linear structure of the wave equations. We shall exhibit how this can be applied in General Relativity for perturbations of the Minkowski space-time governed bytheEinstein-Yang-Mills system in the Lorenz gauge and in wave coordinates, by studying first the simpler case of higher dimensions.