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On the $L^2$-critical nonlinear Schrödinger Equation with a nonlinear damping

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  • We consider the Cauchy problem for the $L^2$-critical nonlinear Schrödinger equation with a nonlinear damping. According to the power of the damping term, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$.
    Mathematics Subject Classification: Primary: 35M11; Secondary: 35A01.


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