Global solutions for the two-dimensional massive Dirac–Klein–Gordon system with a class of large initial data

In this paper, we investigate the global existence and long-time behavior of solutions to the massive Dirac–Klein–Gordon system in R1+2 for a class of large initial data. We establish global existence, sharp pointwise decay estimates and linear scattering under the assumption that only the initial data for the Dirac field are small. This assumption permits the initial data for the Klein–Gordon field to have a finite weighted Sobolev norm, without imposing any restriction on its size. Our analysis is carried out under a natural mass condition, consistent with that appearing in the small-data theory. The main difficulties arise from the presence of large data, the lack of symmetry and the weak decay properties of solutions in two spatial dimensions. To overcome these challenges, we exploit a vanishing structure hidden in the Dirac energy and introduce new dynamical variables that reveal a null structure inherent in the massive Dirac–Klein–Gordon system.