On the L2L^{2}-critical nonlinear Schrödinger Equation with a nonlinear damping

preprint2013arXivOpen access

Abstract

We consider the Cauchy problem for the L2L^{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 ∥∇u(t)∥L2\|\nabla u(t)\|_{L^2}.

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