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

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