Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise
ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 20

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.

DOI : 10.1051/cocv/2022014
Classification : 60H15
Keywords: Irreducibility, Kuramoto-Sivashinsky equation, degenerate noise, approximate controllability, Agrachev-Sarychev method 
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     author = {Gao, Peng},
     title = {Irreducibility of {Kuramoto-Sivashinsky} equation driven by degenerate noise},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {28},
     doi = {10.1051/cocv/2022014},
     mrnumber = {4388378},
     zbl = {1485.60059},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv/2022014/}
}
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Gao, Peng. Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 20. doi: 10.1051/cocv/2022014

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