Nonlinear wave equations
Wave equations are ubiquitous in the description of physical phenomena ranging from compressible fluids (sound waves) to General Relativity (gravitational waves).
The course will propose an introduction to the mathematical theory of nonlinear wave equations, with a focus on global existence and asymptotic dispersive behavior for large time.
Time permitting and depending on students' interests, we will also discuss more advanced applications such as the stability of Minkowski spacetime in General Relativity or the decay of wave equations on black holes.
The course will be based on Jonathan Luk's lecture notes on nonlinear wave equations, available online here: https://web.stanford.edu/~jluk/NWnotes.pdf
Basic knowledge of functional analysis (such as Sobolev embedding) will be assumed.