Global regular solutions for the 3D Zakharov-Kuznetsov equation posed on a bounded domain

TL;DR

This paper proves the existence, uniqueness, and exponential decay of global regular solutions for the 3D Zakharov-Kuznetsov equation on bounded domains, advancing understanding of its long-term behavior.

Contribution

It establishes the first rigorous proof of global regular solutions and their exponential decay for the 3D Zakharov-Kuznetsov equation on bounded domains.

Findings

Existence and uniqueness of global regular solutions.

Exponential decay of the H^2-norm for small initial data.

Results applicable to bounded domain settings.

Abstract

An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on bounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data are proven.