On existence and scattering theory for the Klein–Gordon–Schrödinger system in an infinite $$L^{2}$$L2-norm setting

This paper is concerned with the initial value problem for the nonlinear Klein–Gordon–Schrödinger (KGS) system in $$\mathbb {R}^{n}\times \mathbb {R},\, n\ge 1$$Rn×R,n≥1. We consider general polynomial nonlinearities that include in particular the classical Yukawa–KGS model. We show existence of local and global mild solutions for the KGS system with initial data in weak $$L^{r}$$Lr-spaces, which is an infinite $$L^{2}$$L2-norm setting. Moreover, we obtain a persistence result in $$H^{s}$$Hs when the initial data belong to this class, which shows that the constructed data-solution map in weak-$$L^{r}$$Lr recovers $$H^{s} $$Hs-regularity. We also prove results of scattering and wave operators in that singular framework.