发表机构
Chung-Ang University（中央大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明FPUT系统的一般解在$L^2$中可由两个反向传播的KdV波在$\log(1/h)$时间尺度上近似，结合守恒律与局部适定性理论，并引入频率局部化辅助方程解决范数比较难题。
AI 中文摘要
我们证明，当晶格间距$h$趋于零时，无限Fermi-Pasta-Ulam-Tsingou (FPUT)系统的一般解可以在$L^2$中由两个反向传播的Korteweg-de Vries (KdV)波在$\log(1/h)$阶的时间区间上近似。这解决了第一作者及其合作者提出的一个开放问题~\cite{HKY2021}。我们的证明结合了FPUT守恒律与$L^2$中$h$-一致局部适定理论以及Sobolev正则性的持续性。我们还引入了一个频率局部化的辅助方程，以克服比较与FPUT和KdV流相关的Fourier限制范数的困难。
英文摘要
We prove that, as the lattice spacing $h$ tends to zero, general solutions to the infinite Fermi--Pasta--Ulam--Tsingou (FPUT) system can be approximated in $L^2$ by two counter-propagating Korteweg--de Vries (KdV) waves on time intervals of order $\log(1/h)$. This resolves an open question raised by the first author and collaborators~\cite{HKY2021}. Our proof combines the FPUT conservation law with an $h$-uniform local well-posedness theory in $L^2$ and persistence of Sobolev regularity. We also introduce a frequency-localized auxiliary equation to overcome the difficulty of comparing the Fourier restriction norms associated with the FPUT and KdV flows.
Comments50 pages. Minor revisions; some explanations added and proofs simplified
