Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling
Agus Leonardi Soenjaya
Received October 29, 2020. Published online November 15, 2021.
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 $(u,n)\in L^2\times L^2$ under some conditions on the nonlinearity (the coupling term), by using the $L^2$ 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.
Keywords: low regularity; global well-posedness; Klein-Gordon-Schrödinger equation; higher order coupling