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arXiv · 1912.08752

Blow-up criteria for linearly damped nonlinear Schr\"odinger equations

Van Duong Dinh
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Abstract

We consider the Cauchy problem for linearly damped nonlinear Schr\"odinger equations \[ i\partial_t u + \Delta u + i a u= \pm |u|^\alpha u, \quad (t,x) \in [0,\infty) \times \mathbb{R}^N, \] where $a>0$ and $\alpha>0$. We prove the global existence and scattering for a sufficiently large damping parameter in the energy-critical case. We also prove the existence of finite time blow-up $H^1$ solutions to the focusing problem in the mass-critical and mass-supercritical cases.

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Van Duong Dinh. 2019-12-18. Blow-up criteria for linearly damped nonlinear Schr\"odinger equations. https://arxiv.org/abs/1912.08752

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