Abstract
We introduce control and stabilization issues for fluid flows along with known results in the field. Some models coupling fluid flow equations and equations for rigid or elastic bodies are presented, together with a few controllability and stabilization results.
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. An. IHP, Analyse Non Lin. http://dx.doi.org/10.1016/j.anihpc.2013.03.009
Barbu V, Lasiecka I, Triggiani R (2006) Tangential boundary stabilization of Navier-Stokes equations. Mem Am Math Soc 181 (852) 128
Boulakia M, Guerrero S (2013) Local null controllability of a fluid-solid interaction problem in dimension 3. J Eur Math Soc 15:825–856
Chambolle A, Desjardins B, Esteban MJ, Grandmont C (2005) Existence of weak solutions for unsteady fluid-plate interaction problem. J Math Fluid Mech 7:368–404
Coron J-M (1996) On the controllability of 2-D incompressible perfect fluids. J Math Pures Appl 75(9):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. Comm. P. D. E. 21:573–596
Fernandez-Cara E, Guerrero S, Imanuvilov Yu O, 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 Yu O (1996) Controllability of evolution equations. Lecture notes series, vol 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 Optim 48:5398–5443
Raymond J-P, Thevenet L (2010) Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers. Discret Contin Dyn Syst 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
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag London
About this entry
Cite this entry
Raymond, JP. (2015). Control of Fluids and Fluid-Structure Interactions. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_15
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5058-9_15
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5057-2
Online ISBN: 978-1-4471-5058-9
eBook Packages: EngineeringReference Module Computer Science and Engineering