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arXiv · 2507.01288

Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions

Jun-ichi Segata
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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.

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Jun-ichi Segata. 2025-07-02. Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions. https://arxiv.org/abs/2507.01288

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