Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling

Abstract

Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in (u, n) ∈ L × L under some conditions on the nonlinearity (the coupling term), by using the L conservation law for u and controlling the growth of n via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007) for some exponents to other dimensions and in lower regularity spaces.