# Initial-boundary value problems in a rectangle for two-dimensional Zakharov-Kuznetsov equation

## TL;DR

This paper studies initial-boundary value problems for the 2D Zakharov-Kuznetsov equation in a rectangle, establishing well-posedness, boundary controllability, and long-time decay of solutions.

## Contribution

It introduces new techniques to prove global well-posedness and analyzes controllability and decay for the 2D Zakharov-Kuznetsov equation in bounded domains.

## Key findings

- Proved global well-posedness for weak and regular solutions.
- Established boundary controllability results.
- Demonstrated long-time decay of weak solutions.

## Abstract

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution are established. As applications of the developed technique results on boundary controllability and long-time decay of weak solutions are also obtained.