Well-posedness for the initial value problem associated to the Zakharov–Kuznetsov (ZK) equation in asymmetric spaces

Émile Deléage () and Felipe Linares ()
Additional contact information
Émile Deléage: ENS de Lyon, 35 parvis René Descartes
Felipe Linares: IMPA, Estrada Dona Castorina 110

Partial Differential Equations and Applications, 2023, vol. 4, issue 2, 1-12

Abstract: Abstract We study well-posedness for Zakharov–Kuznetsov and modified Zakharov–Kuznetsov equations in asymmetric spaces. In order to do so, we extend a theory initiated by Kato for the Korteweg-de Vries equation to higher dimensions $$n\ge 2$$ n ≥ 2 . As an application, we prove a result concerning dispersive blow-up for the modified Zakharov–Kuznetsov in dimension 2.

Keywords: Zakharov–Kuznetsov; Asymmetric Spaces; Dispersive Blow-up; Primary 35Q53; Secondary 35B65 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-023-00223-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:4:y:2023:i:2:d:10.1007_s42985-023-00223-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-023-00223-5

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().