Global Solutions and Stability Properties of the 5th Order Gardner Equation

Miguel A. Alejo, Chulkwang Kwak

Research output: Contribution to journalArticlepeer-review

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In this work, we deal with the initial value problem of the 5th-order Gardner equation in R, presenting the local well-posedness result in H2(R). As a consequence of the local result, in addition to H2-energy conservation law, we are able to prove the global well-posedness result in H2(R). Finally as a direct application, we prove that some globally defined functions, e.g. breather solutions of 5th order Gardner equation, are H2(R) stable.

Original languageEnglish
Pages (from-to)575-621
Number of pages47
JournalJournal of Dynamics and Differential Equations
Issue number1
StatePublished - Mar 2023

Bibliographical note

Funding Information:
M. A. was partially funded by Product. CNPq Grant No. 305205/2016-1 and VI PPIT-US program ref. I3C C. Kwak was partially supported by FONDECYT de Postdoctorado 2017 Proyecto No. 3170067 and project France-Chile ECOS-Sud C18E06, and is supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2020R1F1A1A0106876811). The authors are grateful to the editor and anonymous referee for dealing with our manuscript.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Breather
  • Global well-posedness
  • Higher order Gardner equation
  • Integrability
  • Stability


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