  The aim of this paper is to study the long-time dynamics of solutions of the
evolution system \[ \begin{cases} u_{tt} - \Delta u + u +
\eta(-\Delta)^{\frac{1}{2}}u_t + a_{\epsilon}(t)(-\Delta)^{\frac{1}{2}}v_t =
f(u), & \; (x, t) \in \Omega \times (\tau, \infty), \\ v_{tt} - \Delta v +
\eta(-\Delta)^{\frac{1}{2}}v_t - a_{\epsilon}(t)(-\Delta)^{\frac{1}{2}}u_t = 0,
& \; (x, t) \in \Omega \times (\tau, \infty), \end{cases} \] subject to
boundary conditions \[ u = v = 0, \;\; (x, t)\in \partial\Omega\times (\tau,
\infty), \] where $\Omega$ is a bounded smooth domain in $\mathbb{R}^n$, $n
\geq 3$, with the boundary $\partial\Omega$ assumed to be regular enough, $\eta
> 0$ is constant, $a_{\epsilon}$ is a H\"older continuous function and $f$ is a
dissipative nonlinearity. This problem is a non-autonomous version of the well
known Klein-Gordon-Zakharov system. Using the uniform sectorial operators
theory, we will show the local and global well-posedness of this problem in
$H_0^1(\Omega) \times L^2(\Omega) \times H_0^1(\Omega) \times L^2(\Omega)$.
Additionally, we prove existence, regularity and upper semicontinuity of
pullback attractors.
