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

Mohamad Darwich

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arXiv · 1206.6082

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

Mohamad Darwich

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Abstract

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

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Mohamad Darwich. 2013-01-15. On the $L^{2}$-critical nonlinear Schrödinger Equation with a nonlinear damping. https://arxiv.org/abs/1206.6082

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