三维及更高维Zakharov-Kuznetsov方程的次临界适定性结果

IF 0.8 4区数学 Q2 MATHEMATICS

Annales De L Institut Fourier Pub Date : 2020-01-24 DOI:10.5802/aif.3547

S. Herr, S. Kinoshita

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引用次数: 15

摘要

考虑了空间维度$d\geq 3$上的Zakharov-Kuznetsov方程。证明了柯西问题在整个亚临界范围$s>(d-4)/2$内，在$H^s(\mathbb{R}^d)$是局部适定的，并且在端点处是最优的。作为推论，$L^2(\mathbb{R}^3)$的全局适定性和$H^1(\mathbb{R}^4)$的小条件下的全局适定性。

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

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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来源期刊

Annales De L Institut Fourier 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

1 months

期刊介绍： The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French. The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.