### The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity

Herr S, Kinoshita S (2021)
Journal of Evolution Equations 21(2): 2105-2121.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Einrichtung
Abstract / Bemerkung
The Zakharov-Kuznetsov equation in spatial dimension $d\geq 5$ is considered. The Cauchy problem is shown to be globally well-posed for small initial data in critical spaces and it is proved that solutions scatter to free solutions as $t \to \pm \infty$. The proof is based on i) novel endpoint non-isotropic Strichartz estimates which are derived from the $(d-1)$-dimensional Schr\"odinger equation, ii) transversal bilinear restriction estimates, and iii) an interpolation argument in critical function spaces. Under an additional radiality assumption, a similar result is obtained in dimension $d=4$.
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Evolution Equations
Band
21
Ausgabe
2
Seite(n)
2105-2121
ISSN
1424-3199
Page URI
https://pub.uni-bielefeld.de/record/2945549

### Zitieren

Herr S, Kinoshita S. The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity. Journal of Evolution Equations. 2021;21(2):2105-2121.
Herr, S., & Kinoshita, S. (2021). The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity. Journal of Evolution Equations, 21(2), 2105-2121. https://doi.org/10.1007/s00028-021-00671-9
Herr, S., and Kinoshita, S. (2021). The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity. Journal of Evolution Equations 21, 2105-2121.
Herr, S., & Kinoshita, S., 2021. The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity. Journal of Evolution Equations, 21(2), p 2105-2121.
S. Herr and S. Kinoshita, “The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity”, Journal of Evolution Equations, vol. 21, 2021, pp. 2105-2121.
Herr, S., Kinoshita, S.: The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity. Journal of Evolution Equations. 21, 2105-2121 (2021).
Herr, Sebastian, and Kinoshita, Shinya. “The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity”. Journal of Evolution Equations 21.2 (2021): 2105-2121.
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Open Access

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### Quellen

arXiv: 2008.10256