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arXiv · 2607.12270

Effective stability for Hamiltonian PDEs vanishing spectral gaps

Bingqi Yu·Yong Li
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Abstract

This paper studies the effective stability of nearly integrable Hamiltonian PDEs with asymptotically vanishing spectral gaps ($0 < \alpha < 1$). Under a unified high-low frequency decomposition, we construct a modified block clustering partition based on Bourgain's ideas. By leveraging the vanishing of spectral gaps to suppress high-frequency resonant contributions, the overall non-resonance property is maintained under high-regularity weights. This framework is applied to space fractional and fully dispersive Whitham-Schr\"odinger equations, uniformly yielding explicit stability estimates in Gevrey, logarithmic ultra-differentiable, and Sobolev spaces.

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Bingqi Yu, Yong Li. 2026-07-14. Effective stability for Hamiltonian PDEs vanishing spectral gaps. https://arxiv.org/abs/2607.12270

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