Low regularity global well-posedness for the Klein-Gordon-Schrödinger system with the higher-order Yukawa coupling

Abstract

In this paper, we consider the Klein-Gordon-Schrödinger system with the higher-order Yukawa coupling in $ \mathbb{R}^{1+1} $, and prove the local and global well-posedness in $L^2\times H^{1/2}$. The method to be used is adapted from the scheme originally by J. Colliander, J. Holmer, and N. Tzirakis [8] to use the available $L^2$ conservation law of $u$ and control the growth of $n$ via the estimates in the local theory.