On the radius of spatial analyticity for cubic nonlinear Schr\"{o}dinger equation

Achenef Tesfahun

On the radius of spatial analyticity for cubic nonlinear Schr\"{o}dinger equation

Analysis of PDEs 2017-06-16 v1

Authors: Achenef Tesfahun

Abstract

It is shown that the uniform radius of spatial analyticity $\sigma(t)$ of solutions at time $t$ to the 1d, 2d and 3d cubic nonlinear Schr\"{o}dinger equations cannot decay faster than $1/|t|$ as $|t| \to \infty$ , given initial data that is analytic with fixed radius $\sigma_0$ .

Keywords

spatial analyticity radius of analyticity cubic nonlinear Schrödinger equation decay rate initial data

Cite

@article{arxiv.1706.04659,
  title  = {On the radius of spatial analyticity for cubic nonlinear Schr\"{o}dinger equation},
  author = {Achenef Tesfahun},
  journal= {arXiv preprint arXiv:1706.04659},
  year   = {2017}
}

Comments

13, To appear in J. differential equations

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