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 .
Cite this article
Shinya Kinoshita, Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 2, pp. 451–505DOI 10.1016/J.ANIHPC.2020.08.003