  Consider the Klein-Gordon-Zakharov equations in $\mathbb{R}^{1+2}$, and we
are interested in establishing the small global solution to the equations and
in investigating the pointwise asymptotic behavior of the solution. The
Klein-Gordon-Zakharov equations can be regarded as a coupled semilinear wave
and Klein-Gordon system with quadratic nonlinearities which do not satisfy the
null conditions, and the fact that wave components and Klein-Gordon components
do not decay sufficiently fast makes it harder to conduct the analysis. In
order to conquer the difficulties, we will rely on the hyperboloidal foliation
method and a minor variance of the ghost weight method. As a side result of the
analysis, we are also able to show the small data global existence result for a
class of quasilinear wave and Klein-Gordon system violating the null
conditions.
