Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912512977403904 |
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| author | Correia, Simão Kinoshita, Shinya |
| author_facet | Correia, Simão Kinoshita, Shinya |
| contents | We consider the Cauchy problem associated with the modified Zakharov-Kuznetsov equation over $\mathbb{R}^2$. Taking into consideration the associated dispersive effects, we introduce, for $s,a\ge 0$, a two-parameter space $H^{s,a}(\mathbb{R}^2)$, which scales as the classic $H^s$ spaces. In this new class, we prove local well-posedness for $s+a\ge 1/4$, $0<a<1/4$, and global well-posedness and scattering for small data in the case $s=0, \ a=1/4$. These results are shown to be sharp in the sense of $C^3$-flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation Correia, Simão Kinoshita, Shinya Analysis of PDEs We consider the Cauchy problem associated with the modified Zakharov-Kuznetsov equation over $\mathbb{R}^2$. Taking into consideration the associated dispersive effects, we introduce, for $s,a\ge 0$, a two-parameter space $H^{s,a}(\mathbb{R}^2)$, which scales as the classic $H^s$ spaces. In this new class, we prove local well-posedness for $s+a\ge 1/4$, $0<a<1/4$, and global well-posedness and scattering for small data in the case $s=0, \ a=1/4$. These results are shown to be sharp in the sense of $C^3$-flows. |
| title | Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.23397 |