Low Regularity Global Well-Posedness for the Klein-Gordon-Schr\"odinger System with the Higher Order Yukawa Coupling

In this paper, we consider the Klein-Gordon-Schr"{o}dinger system with the higher order Yukawa coupling in ${\mathbb{R}}^{1+1}$, and prove the local and global wellposedness in $L^2\times H^{1\mathrm{/}2}$. The method to be used is adapted from the scheme originally by Colliander J., Holmer J., Tzirakis N. \cite{CoHT06} to use the available $L^2$ conservation law of $u$ and control the growth of $n$ via the estimates in the local theory.