Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions
Jun-ichi Segata
TL;DR
This paper proves the existence of wave operators for the two-dimensional Zakharov-Kuznetsov equation by constructing small global solutions that scatter to free solutions, using the space-time resonance method.
Contribution
It establishes the existence of wave operators for the 2D Zakharov-Kuznetsov equation, advancing understanding of its long-term behavior.
Findings
Existence of wave operators for the 2D Zakharov-Kuznetsov equation.
Construction of small global solutions that scatter to free solutions.
Application of the space-time resonance method to this problem.
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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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Stability and Controllability of Differential Equations