Instability results for supercritical nonlinear wave and Schrödinger equations
Dr. Slim Ibrahim

Abstract: Nonlinear Schrödinger evolutions involve a dynamical balance between linear dispersive spreading of the wave and nonlinear self- interaction of the wave. In sub-critical settings, the dispersive spreading is stronger and therefore solutions are expected to exist globally in time. We show, that in supercritical case, the nonlinear self-interaction of the wave is much stronger. This leads to some sort of instability of the waves.