Nekhoroshev type stability for non-local semilinear Schrödinger equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914369186562048 |
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| author | Yu, Bingqi Yong, Li |
| author_facet | Yu, Bingqi Yong, Li |
| contents | This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schrödinger 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nekhoroshev type stability for non-local semilinear Schrödinger equations Yu, Bingqi Yong, Li Analysis of PDEs Dynamical Systems 35Q55, 37K45, 37J40 This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schrödinger 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. |
| title | Nekhoroshev type stability for non-local semilinear Schrödinger equations |
| topic | Analysis of PDEs Dynamical Systems 35Q55, 37K45, 37J40 |
| url | https://arxiv.org/abs/2512.16299 |