Analysis Seminar

In this talk, we will present some recent results in the study of the nonlinear wave equation with cubic defocusing nonlinearity, describing the completion of a program to establish global well-posedness and scattering in the energy-supercritical regime under an assumed a priori uniform-in-time control of the critical norm. In particular, we discuss a series of recent results in which the concentration-compactness approach of Kenig and Merle is combined with tools from harmonic analysis to yield insight in this class of problems.