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

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 $\mathrm{\parallel }\mathrm{\nabla }u(t){\mathrm{\parallel }}_{L^2}$.