arXiv Open Access 2020

Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher

Sebastian Herr Shinya Kinoshita

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Abstrak

The Zakharov-Kuznetsov equation in space dimension $d\geq 3$ is considered. It is proved that the Cauchy problem is locally well-posed in $H^s(\mathbb{R}^d)$ in the full subcritical range $s>(d-4)/2$, which is optimal up to the endpoint. As a corollary, global well-posedness in $L^2(\mathbb{R}^3)$ and, under a smallness condition, in $H^1(\mathbb{R}^4)$, follow.

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math.AP

Penulis (2)

Sebastian Herr

Shinya Kinoshita

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APA MLA BibTeX

Herr, S., Kinoshita, S. (2020). Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher. https://arxiv.org/abs/2001.09047

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Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓