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

preprint2012arXivOpen access

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

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

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