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

Abstract

We prove that if the difference of two sufficiently smooth solutions of the three-dimensional Zakharov-Kuznetsov equation $$\partial_{t}u+\partial_{x}\triangle u+u\partial_{x}u=0 \text{,}\quad (x,y,z)\in\mathbb R^3, \;t\in[0,1],$$ decays as $e^{-a(x^2+y^2+z^2)^{3/4}}$ at two different times, for some $a>0$ large enough, then both solutions coincide.