哈密顿偏微分方程消失谱隙的有效稳定性
Effective stability for Hamiltonian PDEs vanishing spectral gaps
AI总结：
研究空间分数薛定谔方程在0 < β < 1/2情形下的有效稳定性，利用高低频分解克服渐近频率挑战，能控制近共振误差，还给出了Gevrey类等空间中解的稳定时间估计。
AI中文摘要：
本文研究了具有各种正则性的空间分数薛定谔方程的有效稳定性。研究聚焦于0 < β < 1/2的情形，其以渐近频率为特征。利用高低频分解克服渐近频率的挑战，表明近共振产生的误差可被解的高频部分固有小量控制和有效吸收。此外，该框架统一给出了Gevrey类、对数超可微和有限可微空间中解的稳定时间估计。
英文摘要：
This paper studies the effective stability of nearly integrable Hamiltonian PDEs with asymptotically vanishing spectral gaps ($0 < α< 1$). 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-Schrödinger equations, uniformly yielding explicit stability estimates in Gevrey, logarithmic ultra-differentiable, and Sobolev spaces.
