# To one problem of Saut-Temam for the 3D Zakharov-Kuznetsov equation

## TL;DR

This paper proves the existence, uniqueness, and exponential decay of solutions for a specific initial-boundary value problem related to the 3D Zakharov-Kuznetsov equation on unbounded domains, for small initial data.

## Contribution

It establishes the global regularity and decay properties of solutions to the 3D Zakharov-Kuznetsov equation with new analytical techniques.

## Key findings

- Existence and uniqueness of global regular solutions.
- Exponential decay of the $H^2$-norm for small initial data.
- Results applicable to unbounded domains.

## Abstract

An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on an unbounded domain 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.