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 $L^2\times H^{ 1/2}$. 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.
Categories: math.AP