• Corpus ID: 210911809

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

@article{Herr2020SubcriticalWR,
  title={Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher},
  author={Sebastian Herr and Shinya Kinoshita},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
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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