  We consider the Zakharov-Kutznesov (ZK) equation posed in $\mathbb R^d$, with
$d=2$ and $3$. Both equations are globally well-posed in $L^2(\mathbb R^d)$. In
this paper, we prove local energy decay of global solutions: if $u(t)$ is a
solution to ZK with data in $L^2(\mathbb R^d)$, then \[ \liminf_{t\rightarrow
\infty}\int_{\Omega_d(t)}u^{2}({\bf x},t)\mathrm{d}{\bf x}=0, \] for suitable
regions of space $\Omega_d(t)\subseteq \mathbb R^d$ around the origin, growing
unbounded in time, not containing the soliton region. We also prove local decay
for $H^1(\mathbb R^d)$ solutions. As a byproduct, our results extend decay
properties for KdV and quartic KdV equations proved by Gustavo Ponce and the
second author. Sequential rates of decay and other strong decay results are
also provided as well.
