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

Miguel A. Alejo, Chulkwang Kwak

Research output: Contribution to journalArticlepeer-review

Abstract

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
JournalJournal of Dynamics and Differential Equations
DOIs
StateAccepted/In press - 2021

Keywords

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

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