Abstract

We consider the Zakharov-Kutznesov (ZK) equation posed in (Formula presented.) with d = 2 and 3. Both equations are globally well-posed in (Formula presented.) In this article, we prove local energy decay of global solutions: if u(t) is a solution to ZK with data in (Formula presented.) then (Formula presented.) for suitable regions of space (Formula presented.) around the origin, growing unbounded in time, not containing the soliton region. We also prove local decay for (Formula presented.) 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.