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

  • Shinya Kinoshita

    Universität Bielefeld, Fakultät für Mathematik, Postfach 10 01 31, 33501, Bielefeld, Germany
Global well-posedness for the Cauchy problem of the Zakharov–Kuznetsov equation in 2D cover

A subscription is required to access this article.

Abstract

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. 451–505

DOI 10.1016/J.ANIHPC.2020.08.003