Global boundedness for the nonlinear Klein-Gordon-Schrödinger system with power nonlinearity

Abstract

This paper is concerned with the Cauchy problem of the Klein-Gordon-Schrödinger (KGS) equations with a defocusing nonlinearity in three spatial dimensions. The global wellposedness at $H^2$-regularity level and the growth bounds for the corresponding Sobolev norm of the solutions are obtained by applying Koch-Tzvetkov type Strichartz estimates and modified energy, which removes the restriction of the smallness for the initial data in the previous literature and extends the exponential growth bounds to polynomial case.