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Evolution Equations and Control Theory (EECT)
 

Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension
Pages: 1 - 16, Issue 1, June 2012

doi:10.3934/eect.2012.1.1      Abstract        References        Full text (416.9K)           Related Articles

Viorel Barbu - Octav Mayer Institute of Mathematics (Romanian Academy), Bd. Carol I, no. 8, Iaşi 700505, Romania (email)
Ionuţ Munteanu - Octav Mayer Institute of Mathematics (Romanian Academy), and Alexandru Ioan Cuza University (Department of Mathematics), Bd. Carol I, no. 8, Iaşi 700505, Romania (email)

1 A. V. Balakrishanan, "Applied Functional Analysis," Second editon, Applications of Mathematics, 3, Springer-Verlag, New York-Berlin, 1981.       
2 V. Barbu, Feedback stabilization of Navier-Stokes equations, ESAIM COCV, 9 (2003), 197-206.       
3 V. Barbu and R. Triggiani, Internal stabilization of Navier-Stokes equations with finite dimensional controllers, Indiana Univ. Math. Journal, 53 (2004), 1443-1494.       
4 V. Barbu, I. Lasiecka and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations, Memoires AMS, 851 (2006), x+128 pp.       
5 V. Barbu, R. Triggiani and I. Lasiecka, Abstract settings for tangential boundary stabilization of Navier-Stokes equations by high and low-gain feedback controllers, Nonlin. Anal.,64 (2006), 2704-2746.       
6 V. Barbu, Optimal stabilizable feedback controller for Navier-Stokes equations, in "Nonlinear Analysis and Optimization I. Nonlinear Analysis," Contemp. Math., 513, Amer. Math. Soc., Providence, RI, (2010), 43-53.       
7 V. Barbu and C. Lefter, Internal stabilizability of the Navier-Stokes equations. Optimization and control of distributed systems, Systems and Control Letters, 48 (2003), 161-167.       
8 V. Barbu, "Stabilization of the Navier-Stokes Flows," Springer, New York, 2010.
9 V. Barbu, I. Lasiecka and R. Triggiani, The unique continuation property of eigenfunctions to Stokes-Oseen operator is generic with respect to the coefficients, Nonlin. Anal. Ser. A: Theory Meth. and Appl., to appear.
10 M. Bedra, Feedback stabilization of the 2-D and 3-D Navier Stokes equations based on an extended system, ESAIM COCV, 15 (2009), 934-968.       
11 M. Bedra, Lyapunov functions and local feedback stabilization of the Navier-Stokes equations, SIAM J. Control Optimiz., 48 (2009), 1797-1830.       
12 J.-M. Coron, "Control and Nonlinearity," Mathematical Surveys and Monographs, 136, AMS, Providence, RI, 2007.       
13 A. Fursikov, Stabilization for the 3D Navier-Stokes systems by feedback boundary control, Discrete and Contin. Dyn. Syst., 10 (2004), 289-314.       
14 I. Lasiecka and R. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theory," Cambridge Univ. Press, Cambridge, 2000.
15 J.-P. Raymond, Feedback boundary stabilization of the three-dimensional incompressible Navier-Stokes equations, J. Math. Pures et Appl. (9), 87 (2007), 627-669.       
16 S. S. Ravindran, Reduced-order adaptive controllers for fluid flows using POD, J. Scientific Computing, 15 (2000), 457-478.       
17 A. Shirikyan, Exact controllability in projections for three-dimensional Navier-Stokes equations, Ann. I. H. Poincaré Anal. Non Linéaire, 24 (2007), 521-537.       
18 P. Constantin and C. Foias, "Navier-Stokes Equations," Chicago Lectures in Mathematics, The Univ. of Chicago Press, Chicago, IL, 1988.       

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