turkmath.org

The question of global existence for solutions to the defocusing energy-supercritical nonlinear dispersive equations and wave equations such as the nonlinear Schrodinger and nonlinear wave equation has been a longstanding open question, often thought of as a model problem related to understanding the role of supercritical scaling in the equations of fluid mechanics.

In this talk, I will give an introduction to these PDEs and an overview of what is known about the energy supercritical setting. This will touch on concentration compactness techniques, from which it is by now well-understood that uniform control in the scaling-critical L^2-based homogeneous Sobolev norm prevents finite-time blowup (and indeed implies a scattering result), as well as recent results concerning a construction of finite-time blow up for solutions evolving from certain smooth data due to Merle, et al., and connections with recent work based on a quantitative version (i.e. not based on compactness arguments) of the uniform-critical-control implies scattering results.  The talk will be self-contained and accessible to graduate students from a variety of areas.