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Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
Annales de l'Institut Henri Poincaré C, Analyse non linéaire ( IF 1.8 ) Pub Date : 2020-08-13 , DOI: 10.1016/j.anihpc.2020.08.003 Shinya Kinoshita 1
中文翻译:
二维Zakharov-Kuznetsov方程Cauchy问题的整体适定性
更新日期:2020-08-13
Annales de l'Institut Henri Poincaré C, Analyse non linéaire ( IF 1.8 ) Pub Date : 2020-08-13 , DOI: 10.1016/j.anihpc.2020.08.003 Shinya Kinoshita 1
Affiliation
This paper is concerned with the Cauchy problem of the 2D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness in the Sobolev space for , and these are optimal up to the endpoint. We utilize the nonlinear version of the classical Loomis-Whitney inequality and develop an almost orthogonal decomposition of the set of resonant frequencies. As a corollary, we obtain global well-posedness in .
中文翻译:
二维Zakharov-Kuznetsov方程Cauchy问题的整体适定性
本文涉及二维Zakharov-Kuznetsov方程的柯西问题。我们证明了双线性估计,这暗示了Sobolev空间中时间适定性的局部性 对于 ,这是最佳的端点。我们利用经典Loomis-Whitney不等式的非线性形式,并开发了谐振频率集的几乎正交分解。作为推论,我们获得了。