Non-Linear Wave equations WiSe 2022/23, Gustav Holzegel, Christopher Kauffman

This course is an introduction to the theory of non-linear wave equations. The plan is to cover the following topics:

(1) The linear wave equation in Minkowski space: Representation formula, Fourier techniques, energy estimates, vectorfield method of Klainerman, local existence for general linear equations

(2) Local well-posedness theory non-linear wave equations.

(3) Small data global existence for semi-linear equations with null condition.

(4) Classical blow-up results for semi-linear wave equations

(5) Shock formation results for quasi-linear wave equations (in symmetry)

Some applications to the Einstein equations of general relativity will also be discussed.

Kurs im HIS-LSF