Blowup for the Damped $L^{2}$-Critical Nonlinear Schr\"odinger Equation

Abstract

We consider the Cauchy problem for the $L^{2}$-critical damped nonlinear Schr\"odinger equation. We prove existence and stability of finite time blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$.