(ID: 402 031 2420)

Quasilinear dispersive PDEs often arise in fluid dynamics and plasma physics as effective models. The goal of this lecture series is to provide an introduction to the theory of local well-/ill-posedness of the Cauchy problem for such equations. In the first part, I will cover classical concepts that are relevant to the wellposedness theory of quasilinear evolution equations, such as hyperbolicity, energy estimate, and the continuity of the solution map. In the second part, I will discuss illposedness mechanisms in the dispersive case, and techniques for proving wellposedness in the absence of such obstructions. An emphasis will be given on the phenomenon of degenerate dispersion, which is a strong instability mechanism for conservative quasilinear dispersive PDE.