Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D

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 H-s(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(R-2). (C) 2020 L'Association Publications de l'Institut Henri Poincare. Published by Elsevier B.V. All rights reserved.