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arXiv · 2512.16299

Nekhoroshev type stability for non-local semilinear Schr\"odinger equations

Bingqi Yu·Li Yong
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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.

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Bingqi Yu, Li Yong. 2025-12-18. Nekhoroshev type stability for non-local semilinear Schr\"odinger equations. https://arxiv.org/abs/2512.16299

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