Almost sure scattering for the energy-critical NLS with radial data below $H^1(\mathbb{R}^4)$

Rowan Killip; Jason Murphy; Monica Visan

Almost sure scattering for the energy-critical NLS with radial data below $H^1(\mathbb{R}^4)$

Analysis of PDEs 2019-05-27 v1

Authors: Rowan Killip , Jason Murphy , Monica Visan

Abstract

We prove almost sure global existence and scattering for the energy-critical nonlinear Schr\"odinger equation with randomized spherically symmetric initial data in $H^s(\mathbb{R}^4)$ with $\frac56<s<1$ . We were inspired to consider this problem by the recent work of Dodson--L\"uhrmann--Mendelson, which treated the analogous problem for the energy-critical wave equation.

Keywords

energy-critical nls almost sure scattering radial data randomized initial data global existence nonlinear schrödinger equation spherically symmetric

Cite

@article{arxiv.1707.09051,
  title  = {Almost sure scattering for the energy-critical NLS with radial data below $H^1(\mathbb{R}^4)$},
  author = {Rowan Killip and Jason Murphy and Monica Visan},
  journal= {arXiv preprint arXiv:1707.09051},
  year   = {2019}
}

Comments

19 pages

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