| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 77 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2025063 | |
| Published online | 22 September 2025 | |
Approximate controllability and irreducibility of the 2D Zakharov–Kuznetsov–Burgers equation
School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, PR China
* Corresponding author: chenmochenmo.good@163.com
Received:
22
December
2024
Accepted:
16
July
2025
The present paper is a continuation of [Chen and Rosier, Discrete Continuous Dyn. Syst.- B 25 (2020) 3889–3916] and [Chen, Appl. Math. Optim. 87 (2023) 12]. In this paper, we consider the 2D Zakharov–Kuznetsov–Burgers equation posed on the periodic domain T2. We show that the 2D Zakharov–Kuznetsov–Burgers equation is globally approximately controllable by a finite dimensional external force, the proof is based on the Agrachev–Sarychev approach in geometric control theory. As an application of the approximate controllability result, we establish the irreducibility of the transition semigroup associated with stochastic Zakharov–Kuznetsov–Burgers equation driven by a degenerate noise.
Mathematics Subject Classification: 35Q53 / 93B05 / 60H15
Key words: Zakharov–Kuznetsov–Burgers equation / Agrachev–Sarychev approach / approximate controllability / irreducibility / degenerate noise / geometric control theory
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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