  We are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$,
which is an important model in plasma physics with extensive mathematical
studies. The system can be regarded as semilinear coupled wave and Klein-Gordon
equations with nonlinearities violating the null conditions. Without the
compactness assumptions on the initial data, we aim to establish the existence
of small global solutions, and in addition, we want to illustrate the optimal
pointwise decay of the solutions. Furthermore, we show that the Klein-Gordon
part of the system enjoys linear scattering while the wave part has uniformly
bounded low-order energy. None of these goals is easy because of the slow
pointwise decay nature of the linear wave and Klein-Gordon components in
$\mathbb{R}^{1+2}$. We tackle the difficulties by carefully exploiting the
properties of the wave and the Klein-Gordon components, and by relying on the
ghost weight energy estimates to close higher-order energy estimates. This
appears to be the first pointwise decay result and the first scattering result
for the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$ without compactness
assumptions.

Analysis of PDEs