The HADES seminar on Tuesday, September 5th will be at 3:30pm in Room 740.

Speaker: Sung-Jin Oh

Abstract: In this talk, my aim is to provide a unified viewpoint on two illposedness mechanisms for dispersive equations, namely degenerate dispersion and (the failure of) the Takeuchi-Mizohata condition. For a linear dispersive equation, degenerate dispersion is a property of the principal term in the presence of degenerating coefficients, and the Takeuchi-Mizohata condition concerns the effect of the subprincipal term. First, I will demonstrate how these two effects manifest in the context of wave packet construction. Then, I will exhibit a simple energy and duality argument (similar to testing by wave packets of Ifrim-Tataru) that allows one to extend this illposedness phenomenon to a variety of quasilinear(!) degenerate dispersive PDEs, including singular generalized SQG, surface growth model, Rosenau-Hyman model, etc. This talk is mostly based on joint projects with In-Jee Jeong and Dongho Chae.