Nekhoroshev type stability for Ultra-differential Hamiltonian in $L^2$ space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912773366087680 |
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| author | Yu, Bingqi Yong, Li |
| author_facet | Yu, Bingqi Yong, Li |
| contents | This paper combines the decay of high modes with the smallness introduced by high orders, leading to a normal form lemma for infinite-dimensional Hamiltonian systems under ultra-differentiable regularity. We prove the sub-exponential stability time of a wide class of Hamiltonian PDEs, including the Schrödinger equation with convolution potentials, fractional-order Schrödinger equations, and beam equations with metrics. When the conditions are equivalent to previous ones, the stability time we obtain reaches Bourgain's predicted optimal bound. Furthermore, we approach earlier results under lower conditions. These results are discussed within a general framework we propose, which applies to the ultra-differential class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nekhoroshev type stability for Ultra-differential Hamiltonian in $L^2$ space Yu, Bingqi Yong, Li Analysis of PDEs Dynamical Systems 37K55, 37K45 This paper combines the decay of high modes with the smallness introduced by high orders, leading to a normal form lemma for infinite-dimensional Hamiltonian systems under ultra-differentiable regularity. We prove the sub-exponential stability time of a wide class of Hamiltonian PDEs, including the Schrödinger equation with convolution potentials, fractional-order Schrödinger equations, and beam equations with metrics. When the conditions are equivalent to previous ones, the stability time we obtain reaches Bourgain's predicted optimal bound. Furthermore, we approach earlier results under lower conditions. These results are discussed within a general framework we propose, which applies to the ultra-differential class. |
| title | Nekhoroshev type stability for Ultra-differential Hamiltonian in $L^2$ space |
| topic | Analysis of PDEs Dynamical Systems 37K55, 37K45 |
| url | https://arxiv.org/abs/2512.16332 |