On the instability for the cubic nonlinear Schrodinger equation

Rémi Carles

doi:10.1016/j.crma.2007.03.006

On the instability for the cubic nonlinear Schrodinger equation

偏微分方程分析 2016-08-14 v1

作者: Rémi Carles

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摘要

We study the flow map associated to the cubic Schrodinger equation in space dimension at least three. We consider initial data of arbitrary size in $H^s$ , where $0<s<s_c$ , $s_c$ the critical index, and perturbations in $H^\si$ , where $\si<s_c$ is independent of $s$ . We show an instability mechanism in some Sobolev spaces of order smaller than $s$ . The analysis relies on two features of super-critical geometric optics: creation of oscillation, and ghost effect.

关键词

nonlinear schrödinger equation sobolev regularity of partial differential equations nonlinear schrödinger equations

引用

@article{arxiv.math/0701858,
  title  = {On the instability for the cubic nonlinear Schrodinger equation},
  author = {Rémi Carles},
  journal= {arXiv preprint arXiv:math/0701858},
  year   = {2016}
}

备注

4 pages

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