Department of Mathematics
Kobe University
Kobe, 657-8501, Japan
email: sohsawa@math.kobe-u.ac.jp
Department of Mathematics
Kobe University
Kobe, 657-8501, Japan
email: takaoka@math.kobe-u.ac.jp
Satoshi Osawa, Hideo Takaoka
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
DOI: 10.58997/ejde.2023.05
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| Satoshi Osawa Department of Mathematics Kobe University Kobe, 657-8501, Japan email: sohsawa@math.kobe-u.ac.jp | |
|
Hideo Takaoka Department of Mathematics Kobe University Kobe, 657-8501, Japan email: takaoka@math.kobe-u.ac.jp |
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