| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 86 | |
| Number of page(s) | 25 | |
| DOI | https://doi.org/10.1051/cocv/2025071 | |
| Published online | 08 October 2025 | |
Global approximate controllability of the Camassa–Holm equation by a finite dimensional force
Department of Mathematics and Statistics, Indian Institute of Science Education and Research Kolkata, Mohanpur 741 246, India
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
12
November
2024
Accepted:
16
August
2025
Abstract
In this article, we consider the Camassa–Holm equation posed on the periodic domain T. We show that in any positive time, the Camassa–Holm equation is globally approximately controllable in Hs(T) for s > 3/2 by a three dimensional external force. The proof is based on Agrachev–Sarychev approach in geometric control theory. In particular, our three dimensional control prevents a finite time blow up of the solution of Camassa–Holm equation in Hs(T) for s > 3/2.
Mathematics Subject Classification: 93B05 / 93C20 / 76B15 / 35Q35 / 93B27
Key words: Camassa–Holm equation / approximate controllability / geometric control theory
© The authors. Published by EDP Sciences, SMAI 2025
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