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Feedback stabilization of Navier–Stokes equations

ESAIM: COCV, 9 (2003) 197-205
Published online: 2003-09-15

Feedback Stabilization of Magnetohydrodynamic Equations

Cătălin-George Lefter
SIAM Journal on Control and Optimization 49 (3) 963 (2011)
DOI: 10.1137/070697124

Lyapunov Function and Local Feedback Boundary Stabilization of the Navier–Stokes Equations

SIAM Journal on Control and Optimization 48 (3) 1797 (2009)
DOI: 10.1137/070682630

Boundary feedback stabilization of the monodomain equations

Tobias Breiten and Karl Kunisch
Mathematical Control and Related Fields 7 (3) 369 (2017)
DOI: 10.3934/mcrf.2017013

Feedback stabilization of a thermal fluid system with mixed boundary control

John A. Burns, Xiaoming He and Weiwei Hu
Computers & Mathematics with Applications 71 (11) 2170 (2016)
DOI: 10.1016/j.camwa.2016.01.011

Local Stabilization of the Navier–Stokes Equations with a Feedback Controller Localized in an Open Subset of the Domain

Numerical Functional Analysis and Optimization 28 (5-6) 559 (2007)
DOI: 10.1080/01630560701348434

The internal stabilization by noise of the linearized Navier-Stokes equation

Viorel Barbu
ESAIM: Control, Optimisation and Calculus of Variations 17 (1) 117 (2011)
DOI: 10.1051/cocv/2009042

Boundary Stabilization of Stokes System in Exterior Domains

A. V. Gorshkov
Journal of Mathematical Fluid Mechanics 18 (4) 679 (2016)
DOI: 10.1007/s00021-016-0258-5

Certain questions of feedback stabilization for Navier-Stokes equations

Alexey V. Gorshkov and Andrei Fursikov
Evolution Equations and Control Theory 1 (1) 109 (2012)
DOI: 10.3934/eect.2012.1.109

Boundary stabilization of the Navier-Stokes equations with feedback controller via a Galerkin method

Daniel Y. Le Roux, Abdou Sène and Evrad M. D. Ngom
Evolution Equations and Control Theory 3 (1) 147 (2014)
DOI: 10.3934/eect.2014.3.147

Riccati-Based Feedback Control of the Monodomain Equations With the Fitzhugh--Nagumo Model

Tobias Breiten and Karl Kunisch
SIAM Journal on Control and Optimization 52 (6) 4057 (2014)
DOI: 10.1137/140964552

Finite-dimensional stabilization of stationary Navier-Stokes systems

A. Yu. Chebotarev
Differential Equations 48 (3) 390 (2012)
DOI: 10.1134/S001226611203010X

A feedback control method for the stabilization of a nonlinear diffusion system on a graph

Xin Yu, Chao Xu and Qun Lin
Chinese Physics B 23 (8) 080206 (2014)
DOI: 10.1088/1674-1056/23/8/080206

Motion planning and trajectory tracking for three-dimensional Poiseuille flow

JENNIE COCHRAN and MIROSLAV KRSTIC
Journal of Fluid Mechanics 626 307 (2009)
DOI: 10.1017/S0022112009005977

Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension

Ionuţ Munteanu and Viorel Barbu
Evolution Equations and Control Theory 1 (1) 1 (2012)
DOI: 10.3934/eect.2012.1.1

Feedback boundary stabilization of the three-dimensional incompressible Navier–Stokes equations

J.-P. Raymond
Journal de Mathématiques Pures et Appliquées 87 (6) 627 (2007)
DOI: 10.1016/j.matpur.2007.04.002

Internal Stabilization of a Mutualistic Reaction Diffusion System

Wang Yuan Dong
Acta Mathematica Sinica, English Series 23 (2) 373 (2007)
DOI: 10.1007/s10114-005-0911-z

A Closed-Form Feedback Controller for Stabilization of the Linearized 2-D Navier–Stokes Poiseuille System

Rafael Vazquez and Miroslav Krstic
IEEE Transactions on Automatic Control 52 (12) 2298 (2007)
DOI: 10.1109/TAC.2007.910686

Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control

Discrete and Continuous Dynamical Systems 32 (4) 1169 (2011)
DOI: 10.3934/dcds.2012.32.1169

Abstract settings for tangential boundary stabilization of Navier–Stokes equations by high- and low-gain feedback controllers

Viorel Barbu, Irena Lasiecka and Roberto Triggiani
Nonlinear Analysis: Theory, Methods & Applications 64 (12) 2704 (2006)
DOI: 10.1016/j.na.2005.09.012

Stabilizing Semilinear Parabolic Equations

V. Barbu, D. Coca and Y. Yan
Numerical Functional Analysis and Optimization 26 (4-5) 449 (2005)
DOI: 10.1080/01630560500248272

On a Unique Continuation Property Related to the Boundary Stabilization of Magnetohydrodynamic Equations

Cătălin-George Lefter
Annals of the Alexandru Ioan Cuza University - Mathematics 56 (1) 1 (2010)
DOI: 10.2478/v10157-010-0001-0

Stabilization of equilibrium MHD configurations by external currents

A. Yu. Chebotarev
Computational Mathematics and Mathematical Physics 52 (12) 1670 (2012)
DOI: 10.1134/S0965542512120068

Stabilization of the simplest normal parabolic equation

Andrei Fursikov
Communications on Pure and Applied Analysis 13 (5) 1815 (2014)
DOI: 10.3934/cpaa.2014.13.1815

Internal Optimal Controller Synthesis for Navier–Stokes Equations

Y. Yan, D. Coca and V. Barbu
Numerical Functional Analysis and Optimization 29 (1-2) 225 (2008)
DOI: 10.1080/01630560701872458

Internal Stabilization by Noise of the Navier–Stokes Equation

Viorel Barbu and Giuseppe Da Prato
SIAM Journal on Control and Optimization 49 (1) 1 (2011)
DOI: 10.1137/09077607X

Internal stabilization of semilinear parabolic systems

V. Barbu and G. Wang
Journal of Mathematical Analysis and Applications 285 (2) 387 (2003)
DOI: 10.1016/S0022-247X(03)00405-0

$H^\infty$ Feedback Boundary Stabilization of the Two-Dimensional Navier–Stokes Equations

Sheetal Dharmatti, Jean-Pierre Raymond and Laetitia Thevenet
SIAM Journal on Control and Optimization 49 (6) 2318 (2011)
DOI: 10.1137/100782607

Global stabilization of the Navier-Stokes equations around an unstable equilibrium state with a boundary feedback controller

Daniel Y. Le Roux, Abdou Sène and Evrad M. D. Ngom
Evolution Equations and Control Theory 4 (1) 89 (2015)
DOI: 10.3934/eect.2015.4.89

Internal Nonlinear Predictive Control of Semilinear Parabolic Equations

Lianjun Bai and Daniel Coca
IFAC Proceedings Volumes 44 (1) 5525 (2011)
DOI: 10.3182/20110828-6-IT-1002.01385

Feedback stabilization of 2D Navier–Stokes equations with Navier slip boundary conditions

Cătălin Lefter
Nonlinear Analysis: Theory, Methods & Applications 70 (1) 553 (2009)
DOI: 10.1016/j.na.2007.12.026

Algebraic Multiplicities Arising from Static Feedback Control Systems of Parabolic Type

Takao Nambu
Numerical Functional Analysis and Optimization 35 (10) 1359 (2014)
DOI: 10.1080/01630563.2014.884581

Finite-dimensional stabilization of viscous gas dynamics at a given rate

E. V. Amosova
Differential Equations 50 (8) 1080 (2014)
DOI: 10.1134/S0012266114080072

Boundary scalar controllability in projections for the Navier-Stokes system

A. Yu. Chebotarev
Differential Equations 49 (12) 1629 (2013)
DOI: 10.1134/S0012266113120161

Feedback Boundary Stabilization of the Two-Dimensional Navier--Stokes Equations

Jean-Pierre Raymond
SIAM Journal on Control and Optimization 45 (3) 790 (2006)
DOI: 10.1137/050628726

Finite-dimensional controllability for systems of Navier-Stokes type

A. Yu. Chebotarev
Differential Equations 46 (10) 1498 (2010)
DOI: 10.1134/S0012266110100149

Internal Exponential Stabilization to a Nonstationary Solution for 3D Navier–Stokes Equations

Viorel Barbu, Sérgio S. Rodrigues and Armen Shirikyan
SIAM Journal on Control and Optimization 49 (4) 1454 (2011)
DOI: 10.1137/100785739