Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise

被引：1

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.

引用

页数：22

共 46 条

[41] NON-LINEAR ANALYSIS OF HYDRODYNAMIC INSTABILITY IN LAMINAR FLAMES .1. DERIVATION OF BASIC EQUATIONS [J].