# Regular Solutions to Initial-Boundary Value Problems in a Half-Strip for Two-Dimensional Zakharov-Kuznetsov Equation

## TL;DR

This paper investigates the existence, regularity, and decay of solutions to initial-boundary value problems for the two-dimensional Zakharov-Kuznetsov equation in a half-strip, covering various boundary conditions.

## Contribution

It provides new results on global well-posedness, internal regularity, and long-time decay of solutions for different boundary conditions in a half-strip setting.

## Key findings

- Global well-posedness for periodic and Neumann conditions
- Internal regularity of solutions for all boundary types
- Long-time decay of solutions under Dirichlet conditions

## Abstract

Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of periodic and Neumann boundary conditions, as well as on internal regularity of solutions for all types of boundary conditions are established. Also in the case of Dirichlet boundary conditions one result on long-time decay of regular solutions is obtained.