Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911033581371392 |
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| author | Segata, Jun-ichi |
| author_facet | Segata, Jun-ichi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_01288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions Segata, Jun-ichi Analysis of PDEs 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. |
| title | Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.01288 |