Internal stabilization of Navier-Stokes equations with finite-dimensional controllers

被引：116

作者：

Barbu, V ^{[1
]}

Triggiani, R

机构：

[1] Univ Al I Cuza, Dept Math, Iasi 6600, Romania

[2] Univ Virginia, Dept Math, Charlottesville, VA 22903 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2004年 / 53卷 / 05期

关键词：

Navier-Stokes equations; stabilization; Riccati equation; steady-state solution; feedback controller;

D O I：

10.1512/iumj.2004.53.2445

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The steady-state solutions to Navier-Stokes equations on Omega subset of R-,(d) d = 2, 3, with no-slip boundary conditions, are locally exponentially stabilizable by a finite-dimensional feedback controller with support in an arbitrary open subset omega subset of Omega of positive measure. The (finite) dimension of the feedback controller is related to the largest algebraic multiplicity of the unstable eigenvalues of the linearized equation.

引用

页码：1443 / 1494

页数：52

共 19 条

[1]

[Anonymous], SHELL MODEL APPL NUC

[2]

[Anonymous], 1966, GRUNDLEHREN MATH WIS

[3]

[Anonymous], 1983, APPL MATH SCI, DOI DOI 10.1007/978-1-4612-5561-1

[4]

[Anonymous], AM MATH SOC TRANSL 2

[5] Internal stabilization of semilinear parabolic systems [J].

Barbu, V ;

Wang, G .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 285 (02) :387-407

[6] Feedback stabilization of Navier-Stokes equations [J].

Barbu, V .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2003, 9 (09) :197-206

[7]

BARBU V, 2003, ABSTR APPL ANAL, P697

[8]

BARBU V, 2004, BOUNDARY STABILIZATI

[9] Numerical criterion for the stabilization of steady states of the Navier-Stokes equations [J].

Cao, C ;

Kevrekidis, IG ;

Titi, ES .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2001, 50 :37-96

[10]

Constantin P., 1988, CHICAGO LECT MATH

← 1 2 →