Joint Colloquium/Applied math/Analysis talk

Title: Singularity Formation in Nonlinear Derivative Schrödinger Equations

Speaker:  Gideon Simpson, Drexel University 

Abstract: Direct numerical simulation of an $L^2$ supercritical variant of the derivative nonlinear Schrödinger equation suggests that there is a finite time singularity. Subsequent exploration with the dynamic rescaling method provided more detail about the blowup and a recent refined asymptotic analysis of the blowup solution gives predictions of the blowup rates. Due to the mixed hyperbolic-dispersive nature of the equation, these methods have limited the proximity to the blowup time. Using a locally adaptive meshing method, we are able to overcome these difficulties.