Uniqueness results for Zakharov-Kuznetsov equation

TL;DR

This paper establishes conditions under which solutions to the Zakharov-Kuznetsov equation in plasma physics are unique, based on decay properties at two different times, contributing to the mathematical understanding of this PDE.

Contribution

It proves a new uniqueness theorem for the Zakharov-Kuznetsov equation using decay conditions at two times, enhancing the theoretical framework for this PDE.

Findings

Solutions are unique if they decay sufficiently fast at two distinct times.

The result applies to sufficiently regular solutions of the Zakharov-Kuznetsov equation.

The theorem provides a new criterion for solution uniqueness based on decay properties.

Abstract

In this paper we study uniqueness properties of solutions to the Zakharov-Kuznetsov equation of plasma physic. Given two sufficiently regular solutions $u_1, u_2,$ we prove that, if $u_1-u_2$ decays fast enough at two distinct times, then $u_1\equiv u_2.$