Degenerate Dispersion and Illposedness for Generalized SQG Equations

Given a linear equation whose principal term is given by a degenerate dispersive pseudo-differential operator, we provide a framework for the construction of degenerating wave packet solutions. As an application, we prove strong ill-posedness for the generalized SQG equations with singular velocities, which shows sharpness of existing well-posedness results. Joint work with D. Chae and S.-J. Oh.