Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise

被引：0
作者：
Gao, Peng [1 ,2 ]
机构：
[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China
[2] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Changchun 130024, Peoples R China
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2022年 / 28卷
关键词：
Irreducibility; Kuramoto-Sivashinsky equation; degenerate noise; approximate controllability; Agrachev-Sarychev method; NAVIER-STOKES EQUATIONS; NULL-CONTROLLABILITY; TRAJECTORIES; DYNAMICS;
D O I：
10.1051/cocv/2022014
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
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页数：22
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