Nekhoroshev type stability for non-local semilinear Schr\"odinger equations
Abstract
This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schr\"odinger equations with non-local nonlinear terms, employing the method of rational normal forms. We establish the first rigorous results for logarithmic ultra-differentiable regularity in infinite-dimensional Hamiltonian systems without external parameters. Under Gevrey class regularity assumptions, we achieve the stability times matching Bourgain's conjectured optimal stability time in \cite{B04}. Furthermore, we introduce a novel global vector field norm adapted to the rational normal form framework. This norm eliminate the need for degree tracking during the iteration process, thereby enabling a unified treatment of nonlinear terms.
Keywords
Cite
@article{arxiv.2512.16299,
title = {Nekhoroshev type stability for non-local semilinear Schr\"odinger equations},
author = {Bingqi Yu and Li Yong},
journal= {arXiv preprint arXiv:2512.16299},
year = {2026}
}