Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions
Analysis of PDEs
2025-07-03 v1
Abstract
In this paper, we study long time behavior of solution to the two dimensional Zakharov-Kuznetsov equation in the framework of the final state problem. We construct a small global solution to the Zakharov-Kuznetsov equation which scatters to a given free solution. From this result, we have the existence of wave operators for the Zakharov-Kuznetsov equation. The proof is based on the space-time resonance method developed by Gustafson-Nakanishi-Tsai and Germain-Masmoudi-Shatah etc.
Keywords
Cite
@article{arxiv.2507.01288,
title = {Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions},
author = {Jun-ichi Segata},
journal= {arXiv preprint arXiv:2507.01288},
year = {2025}
}