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- W3049673885 abstract "This paper is concerned with the Cauchy problem of the $2$D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness in the Sobolev space $H^s({mathbb{R}}^2)$ for $s > -1/4$, 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 $L^2({mathbb{R}}^2)$." @default.
- W3049673885 created "2020-08-21" @default.
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- W3049673885 date "2021-04-01" @default.
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- W3049673885 title "Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D" @default.
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- W3049673885 doi "https://doi.org/10.1016/j.anihpc.2020.08.003" @default.
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