Videos

Dispersive blow up for nonlinear Schrödinger equations

Presenter
November 1, 2016
Keywords:
  • nonlinear Schrödinger equations, blow-up, dispersion, global smoothing
Abstract
The possibility of finite-time, dispersive blow up for nonlinear equations of Schrödinger type is revisited. We extend earlier results in the literature to include the multi-dimensional case, as well as the case of Davey-Stewartson and Gross-Pitaevskii equations. As a by-product of our analysis, a sharp global smoothing estimate for the integral term appearing in Duhamel’s formula is obtained.