Blowup for the Damped $L^2$-Critical Nonlinear Schrödinger Equation

Abstract

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

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