Some remarks on the nonlinear Schr\"odinger equation with fractional dissipation

Mohamad Darwich; Luc Molinet

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arXiv · 1511.08577

Some remarks on the nonlinear Schr\"odinger equation with fractional dissipation

Mohamad Darwich·Luc Molinet

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Abstract

We consider the Cauchy problem for the $L^2$-critical nonlinear Schr\"odinger equation with a fractional dissipation. According to the order of the fractional dissipation, 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, Luc Molinet. 2015-11-27. Some remarks on the nonlinear Schr\"odinger equation with fractional dissipation. https://arxiv.org/abs/1511.08577

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