Stability enhancement of a 2-D linear Navier-stokes channel flow by a 2-D, wall-normal boundary controller

Discrete and Continuous Dynamical Systems - Series B

Volumn 8, Issue 2, 2007, Pages 279-314

  Triggiani, Roberto ^a  

^a University of Virginia   (United States)

Author keywords

Linear Navier Stokes channel flow; Stability enhancement

Indexed keywords

EID: 35248891524     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.8.279     Document Type: Article

References (21)

1. Aamo, M. Krstic and T. R. Bewley, Control of mixing by boundary feedback in a SD-channel, Automatica 39 (2003), 1597-1606.
2. L. Andrews, "Elementary Partial Differential Equations with Boundary Value Problems," Academic Press, 1986.
3. A. Balogh, W. J. Liu and M. Krstic, Stability enhancement by boundary control in 2D channel flow, IEEE Transaction on Automatic Control, 46 (2001), 1696-1711.
4. V. Barbu, Stabilization of a plane channel flow by wall normal controllers, preprint 2005.
5. V. Barbu, I. Lasiecka and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations, Memoirs AMS, 122 (2006).
6. V. Barbu, I. Lasiecka and R. Triggiani, Abstract settings for tangential boundary stabilization of Navier-Stokes equations by high- and low-gain feedback controllers, J. Nonlinear Analysis, 64 (2006), 2704-2746.
7. V. Barbu, I. Lasiecka and R. Triggiani, Local exponential stabilization strategies of the Navier-Stokes equations, d = 2, 3, via feedback stabilization of its linearization, Proceedings of Oberwolfach Conference, 2005, to appear.
8. V. Barbu and R. Triggiani, Internal stabilization of Navier-Stokes equations with finitely many controllers, Indiana Univ. Math. J., 53 (2004), 1443-1494.
9. P. Constantin and C. Foias, "Navier-Stokes Equations," University of Chicago Press, Chicago-London, 1989.
10. L. R. Keefe, Method and apparatus for reducing the drag of flows over surfaces, US Patent US5803409, 1998.
11. I. Lasiecka, D. Lukes and L. Pandolfi, Input dynamics and non-standard Riccati equations, J. Optimiz. Theory & Appl., 84 (1995), 549-574.
12. I. Lasiecka, L. Pandolfi and T. Triggiani, A singular control approach to highly damped second-order abstract equations and applications, Appl. Math. & Optim., 36 (1997), 67-107.
13. I. Lasiecka and T. Triggiani, "Differential and Algebraic Riccati Equations with Applications to Boundary/Point Control Problems: continuous Theory and Approximation Theory," NCIS, Springer Verlag, N. 164 (1991), page 160.
14. I. Lasiecka and T. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theories I: Abstract Parabolic Systems," Encyclopedia of Mathematics and its Applications 74, Cambridge University Press, 2002, page 648.
15. J. P. Raymond, Feedback boundary stabilization of the two dimensional Navier-Stokes equations, preprint 2005.
16. R. Teman, "Navier-Stokes Equations," North Holland, 1979.
17. R. Triggiani, On the stabilizability problem in Banach spaces, J. Math. Anal. & Appl., (1975), 383-403.
18. R. Triggiani, Boundary feedback stabilizability of parabolic equations, Appl. Math. Optimiz., 6 (1980), 201-220.
19. R. Triggiani, Optimal boundary control and new Riccati equations for highly damped second-order equations, Diff. & Ing. Eqns., 7 (1994), 1109-1144. Invited paper for special volume in memory of P. Hess.
20. R. Vazquez and M. Krstic, A closed-form feedback controller for stabilization of linearized Navier-Stokes equations: the 2D Poissenille flow, preprint 2005.
21. E. Zauderer, "Partial Differential Equations of Applied Mathematics," second edition, 1989, John Wiley & Sons, A Wiley-Interscience Publication.