Subcritical well-posedness results for the Zakharov–Kuznetsov equation in dimension three and higher
Annales de l'Institut Fourier, Online first, 65 p.

The Zakharov–Kuznetsov equation in space dimension d3 is considered. It is proved that the Cauchy problem is locally well-posed in H s ( 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 ( 3 ) and, under a smallness condition, in H 1 ( 4 ), follow.

On considère l’équation de Zakharov–Kuznetsov en dimension d3. On établit que le problème de Cauchy est localement bien posé dans H s pour tout exposant sous-critique s>(d-4)/2. Ceci est optimal jusqu’au cas limite. Comme corollaire, il s’ensuit que l’équation est globalement bien posée dans L 2 ( 3 ) et, sous une hypothèse de petitesse, dans H 1 ( 4 ).

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DOI: 10.5802/aif.3547
Classification: 35Q55
Keywords: Well-posedness, Cauchy problem, Zakharov–Kuznetsov equation, bilinear estimate, nonlinear Loomis–Whitney inequality.
Herr, Sebastian 1; Kinoshita, Shinya 2

1 Universität Bielefeld Fakultät für Mathematik Postfach 10 01 31 33501 Bielefeld (Germany)
2 Department of Mathematics Graduate School of Science and Engineering Saitama University Saitama 338-8570 (Japan)
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Herr, Sebastian; Kinoshita, Shinya. Subcritical well-posedness results for the Zakharov–Kuznetsov equation in dimension three and higher. Annales de l'Institut Fourier, Online first, 65 p.

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