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 $\|\nabla u(t)\|_{L^2}$. 
Mohamad Darwich
math.AP