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

Herr S, Kinoshita S (Submitted) .

Preprint | Eingereicht | Englisch

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Einrichtung
Abstract / Bemerkung
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.
Erscheinungsjahr
2020
Page URI
https://pub.uni-bielefeld.de/record/2940435

### Zitieren

Herr S, Kinoshita S. Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher. Submitted.
Herr, S., & Kinoshita, S. (Submitted). Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
Herr, S., and Kinoshita, S. (Submitted). Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher.
Herr, S., & Kinoshita, S., Submitted. Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher.
S. Herr and S. Kinoshita, “Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher”, Submitted.
Herr, S., Kinoshita, S.: Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher. (Submitted).
Herr, Sebastian, and Kinoshita, Shinya. “Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher”. (Submitted).

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### Quellen

arXiv: 2001.09047