250134 VO Dispersive wave equations (2018S)

Dispersive equations are a very active area of research in the modern theory of partial differential equations with many crosslinks to physics. At least two Fields medals have been awarded for breakthrough contributions to dispersive PDEs and some of the strongest mathematicians worldwide are working in this field.
The course gives a gentle introduction to the theory of nonlinear dispersive wave equations. The main topics include basic well-posedness theory, tools from harmonic analysis (Calderon-Zygmund theory, Littlewood-Paley decomposition), Strichartz estimates, optimal local well-posedness, finite-time blowup, concentration-compactness techniques and stability theory. We will develop everything from scratch and the prerequisites are kept at a bare minimum. Nevertheless, we will make our way up to the forefront of current research.