AI 中文总结
该研究证明非相对论极限下Klein-Gordon-Schrödinger系统在长时间区间上最优收敛到解耦线性Schrödinger方程，收敛速率为O(ε²)，与初始误差阶数一致，匹配数值结果。
AI 中文摘要
本文研究非相对论 regime ε→0下的Klein-Gordon-Schrödinger系统，其中ε与光速的倒数成正比。我们证明，在量级为ε⁻¹的长时间区间上，该系统收敛到一组解耦的线性Schrödinger方程，误差估计形式为(1+t)ε²；特别地，Schrödinger分量的误差估计在时间上一致，形式为ε²。这些误差估计的具体形式与Bao等人展示的数值结果一致，且O(ε²)收敛速率与初始误差的阶数一致，因此是最优的。
英文摘要
In this paper, we study the Klein-Gordon-Schrödinger system in the nonrelativistic regime $ε\to 0$, where $ε$ is proportional to the inverse of the speed of light. We show that the Klein-Gordon-Schrödinger system converges to a system of decoupled linear Schrödinger equations over a long time interval of order $ε^{-1}$ with error estimates of the form $(1+t)ε^2$; in particular, the error estimate for the Schrödinger component is uniform in time of the form $ε^{2}$ The specific forms of the error estimates coincide with the numerical results shown by Bao et a.l., and the $O(ε^{2})$ convergence rates coincide with the order of initial error, and thus are optimal.
Comments25 pages
