Global well-posedness for Cauchy problems of Zakharov-Kuznetsov equations on cylindrical spaces

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 For more information see https://ejde.math.txstate.edu/Volumes/2024/05/abstr.html