Critical 2D Zakharov-Kuznetsov equation posed on a half-strip

TL;DR

This paper studies the critical 2D Zakharov-Kuznetsov equation on a half-strip, proving existence, uniqueness, and exponential decay of solutions for small initial data.

Contribution

It establishes the global well-posedness and decay properties of solutions to the critical 2D Zakharov-Kuznetsov equation on a half-strip, which was previously unaddressed.

Findings

Existence of global regular solutions for small initial data

Uniqueness of solutions in the considered setting

Exponential decay rate of solutions over time

Abstract

An initial-boundary value problem for the critical generalized 2D Zakharov-Kuznetsov equation posed on a half-strip is considered. Existence, uniqueness and the exponential decay rate of global regular solutions for small initial data are established.