  We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We
show global existence of the solutions, as well as sharp time decay and linear
scattering. One key advance is that we provide the first asymptotic stability
result for the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions in the
case of a massive Klein-Gordon field and a massless Dirac field. The
nonlinearities are below-critical in two spatial dimensions, and so our method
requires the identification of special structures within the system and novel
weighted energy estimates. Another key advance, is that our proof allows us to
weaken certain conditions on the nonlinear structures that have been assumed in
the literature.

Analysis of PDEs