| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 20 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/cocv/2022014 | |
| Published online | 03 March 2022 | |
Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise
School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University,
Changchun
130024, PR China.
* Corresponding author: gaopengjilindaxue@126.com
Received:
17
January
2021
Accepted:
11
February
2022
In this paper, we study irreducibility of Kuramoto-Sivashinsky equation which is driven by an additive noise acting only on a finite number of Fourier modes. In order to obtain the irreducibility, we first investigate the approximate controllability of Kuramoto-Sivashinsky equation driven by a finite-dimensional force, the proof is based on Agrachev-Sarychev type geometric control approach. Next, we study the continuity of solving operator for deterministic Kuramoto-Sivashinsky equation. Finally, combining the approximate controllability with continuity of solving operator, we establish the irreducibility of Kuramoto-Sivashinsky equation.
Mathematics Subject Classification: 60H15
Key words: Irreducibility / Kuramoto-Sivashinsky equation / degenerate noise / approximate controllability / Agrachev-Sarychev method
© The authors. Published by EDP Sciences, SMAI 2022
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