Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 05, pp. 1-25.

Title: Global well-posedness for Cauchy problems of Zakharov-Kuznetsov equations on cylindrical spaces
       
Authors: Satoshi Osawa (Kobe Univ., Kobe, Japan)
         Hideo Takaoka (Kobe Univ., Kobe, Japan)

Abstract: 
We study the global well-posedness of the Zakharov-Kuznetsov equation on
cylindrical spaces. Our goal is to establish the existence of global-in-time solutions
below the energy class. To prove the results, we adapt the I-method to extend the
local solutions globally in time. The main tool in our argument is multilinear
estimates in the content of Bourgain's spaces. Using modified energies induced
by the I-method, we obtain polynomial bounds on the $H^s$ growth of global solutions.

Submitted January 3, 2024. Published January 22, 2024.
Math Subject Classifications: 35Q53, 42B37.
Key Words: Zakharov-Kuznetsov equation; low regularity; global well-posedness; bilinear estimate