Abstract
In this entry, some fluid models are introduced, and corresponding controllability and stabilization results are presented. A short overview on control results for fluid-structure interaction models is then given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Bibliography
Alouges F, DeSimone A, Lefebvre A (2008) Optimal strokes for low Reynolds number swimmers: an example. J Nonlinear Sci 18:277–302
Badra M (2009) Lyapunov function and local feedback boundary stabilization of the Navier-Stokes equations. SIAM J Control Optim 48:1797–1830
Badra M, Takahashi T (2013) Feedback stabilization of a simplified 1d fluid-particle system. Ann Inst H Poincaré Anal Non Linéaire. https://doi.org/10.1016/j.anihpc.2013.03.009
Barbu V, Lasiecka I, Triggiani R (2006) Tangential boundary stabilization of Navier-Stokes equations. Memoirs of the American Mathematical Society, vol 181. American Mathematical Society, Providence
Boulakia M, Guerrero S (2013) Local null controllability of a fluid-solid interaction problem in dimension 3. J EMS 15:825–856
Chambolle A, Desjardins B, Esteban MJ, Grandmont C (2005) Existence of weak solutions for unsteady fluid-plate interaction problem. JMFM 7:368– 404
Coron J-M (1996) On the controllability of 2-D incompressible perfect fluids. J Math Pures Appl (9) 75: 155–188
Coron J-M (2007) Control and nonlinearity. American Mathematical Society, Providence
Ervedoza S, Glass O, Guerrero S, Puel J-P (2012) Local exact controllability for the one-dimensional compressible Navier-Stokes equation. Arch Ration Mech Anal 206:189–238
Fabre C, Lebeau G (1996) Prolongement unique des solutions de l’équation de Stokes. Commun Partial Differ Equs 21:573–596
Fernandez-Cara E, Guerrero S, Imanuvilov OY, Puel J-P (2004) Local exact controllability of the Navier-Stokes system. J Math Pures Appl 83:1501– 1542
Fursikov AV (2004) Stabilization for the 3D Navier-Stokes system by feedback boundary control. Partial differential equations and applications. Discrete Contin Dyn Syst 10:289–314
Fursikov AV, Imanuvilov OY (1996) Controllability of evolution equations. Lecture Notes Series, 34. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul
Lequeurre J (2013) Null controllability of a fluid-structure system. SIAM J Control Optim 51:1841–1872
Raymond J-P (2006) Feedback boundary stabilization of the two dimensional Navier-Stokes equations. SIAM J Control Optim 45:790–828
Raymond J-P (2007) Feedback boundary stabilization of the three-dimensional incompressible Navier-Stokes equations. J Math Pures Appl 87:627–669
Raymond J-P (2010) Feedback stabilization of a fluid–structure model. SIAM J Control and Optim 48(8):5398–5443
Raymond J-P, Thevenet L (2010) Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers. DCDS-A 27:1159–1187
Vazquez R, Krstic M (2008) Control of turbulent and magnetohydrodynamic channel flows: boundary Stabilization and estimation. Birkhäuser, Boston
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
Raymond, JP. (2021). Control of Fluid Flows and Fluid-Structure Models. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-44184-5_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44183-8
Online ISBN: 978-3-030-44184-5
eBook Packages: Intelligent Technologies and RoboticsReference Module Computer Science and Engineering