An initial-boundary value problem for three-dimensional Zakharov-Kuznetsov equation

TL;DR

This paper studies a three-dimensional Zakharov-Kuznetsov equation with specific boundary conditions, proving the existence, uniqueness, and decay of solutions over time in weighted spaces.

Contribution

It establishes the first results on global solutions and their decay properties for this equation under homogeneous Dirichlet boundary conditions.

Findings

Proved global existence of weak solutions.

Established uniqueness of solutions.

Demonstrated large-time decay in weighted spaces.

Abstract

An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain weighted spaces are established.