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 language | English |
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Pages (from-to) | 575-621 |
Number of pages | 47 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 35 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2023 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Breather
- Global well-posedness
- Higher order Gardner equation
- Integrability
- Stability