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In this paper, we are interested in the two-dimensional Dirac-Klein-Gordonsystem, which is a basic model in particle physics. We investigate the globalbehaviors of small data solutions to this system in the case of a massivescalar field and a massless Dirac field. More precisely, our main result istwofold: 1) we show sharp time decay for the pointwise estimates of thesolutions which imply the asymptotic stability of this system; 2) we show thelinear scattering result of this system which is a fundamental problem when itis viewed as dispersive equations. Our result is valid for general small,high-regular initial data, in particular, there is no restriction on thesupport of the initial data.

Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations