English

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}
}