On the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation

Abstract

The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation. On the other hand, the main core of the work is devoted to providing an alternative proof of the aforementioned result. The importance of this original contribution relies on the fact that, unlike the approach used in [4], the strategy adopted here is not sensitive of the two dimensional setting of the problem and therefore could be adapted to higher dimensional Zakharov-Kuznetsov equations for which, as far as we know, a proof of an analogous optimal unique continuation principle is still missing. For sake of clearness we focus here on the 2D case only, the higher dimensional analysis will be discussed somewhere else.