Global stability of the Dirac–Klein–Gordon system in two and three space dimensions

In this paper we study global nonlinear stability for the Dirac–Klein–Gordon system in two and three space dimensions for small and regular initial data. In the case of two space dimensions, we consider the Dirac–Klein–Gordon system with a massless Dirac field and a massive scalar field, and prove global existence, sharp time decay estimates and linear scattering for the solutions. In the case of three space dimensions, we consider the Dirac–Klein–Gordon system with a mass parameter in the Dirac equation, and prove uniform (in the mass parameter) global existence, unified time decay estimates and linear scattering in the top order energy space.