Approximate controllability of three-dimensional Navier-Stokes equations

Communications in Mathematical Physics

Volumn 266, Issue 1, 2006, Pages 123-151

  Shirikyan, Armen ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745613246     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0007-3     Document Type: Article

References (23)

1. [AS86] Agrachev, A.A., Sarychev, A.V.: Reduction of a smooth system that is linear with respect to the control. Mat. Sb. (N.S.) 130(172) no. 1, 18-34, 128 (1986)
2. [AS04] Agrachev, A.A., Sachkov, Yu.L.: Control Theory from Geometric Viewpoint. Berlin: Springer-Verlag, 2004
3. [AS05a] Agrachev, A.A., Sarychev, A.V.: Navier-Stokes equations: controllability by means of low modes forcing. J. Math. Fluid Mech. 7, 108-152 (2005)
4. [AS05b] Agrachev, A.A., Sarychev, A.V.: Personal communication
5. [BS01] Barbu, V., Sritharan, S.S.: Flow invariance preserving feedback controllers for the Navier-Stokes equation. J. Math. Anal. Appl. 255(1), 281-307 (2001)
6. [BT04] Barbu, V., Triggiani, R.: Internal stabilization of Navier-Stokes equations with finite-dimensional controllers. Indiana Univ. Math. J. 53(5), 1443-1494 (2004)
7. [CF88] Constantin, P., Foias, C.: Navier-Stokes Equations. Chicago, IL: University of Chicago Press, 1988
8. [CF96] Coron, J.-M., Fursikov, A. V.: Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary. Russ. J. Math. Phys. 4(4), 429-448 (1996)
9. [Cor99] Coron, J.-M.: On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain. SIAM J. Control Optim. 37(6), 1874-1896 (1999) (electronic)
10. [Cor96] Coron, J.-M.: On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions. ESAIM Contrôle Optim. Calc. Var. 1, 35-75 (1995/96) (electronic)
11. [FC99] Fernández-Cara, E.: On the approximate and null controllability of the Navier-Stokes equations. SIAM Rev. 41(2), 269-277 (1999) (electronic)
12. [FE99.] Fursikov, A.V., Emanuilov, O.Yu.: Exact controllability of the Navier-Stokes and Boussinesq equations. Usp. Mat. Nauk 54(3) (327), 93-146 (1999)
13. [Fur95] Fursikov, A.V.: Exact boundary zero controllability of three-dimensional Navier-Stokes equations. J. Dynam. Control Systems 1(3), 325-350 (1995)
14. [Fur01] Fursikov, A.V.: Stabilizability of two-dimensional Navier-Stokes equations with help of aboundary feedback control. J. Math. Fluid Mech. 3(3), 259-301 (2001)
15. [Fur04] Fursikov, A.V.: Stabilization for the 3D Navier-Stokes system by feedback boundary control. Discrete Contin. Dyn. Syst. 10(1-2), 289-314 (2004)
16. [Gla00] Glass, O.: Exact boundary controllability of 3-D Euler equation. ESAIM Control Optim. Calc. Var. 5, 1-44 (2000) (electronic)
17. [Hen81] Henry, D.: Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Berlin: Springer-Verlag, 1981
18. [Ima98] Imanuvilov, O.Yu.: On exact controllability for the Navier-Stokes equations. ESAIM Control Optim. Calc. Var. 3, 97-131 (1998) (electronic)
19. [Jur97] Jurdjevic, V.: Geometric Control Theory. Cambridge: Cambridge University Press, 1997
20. [Lio90] Lions, J.-L.: Remarques sur la contrôlabilité approchée. Spanish-French Conference on Distributed-Systems Control. Malaga: Univ. Malaga, 1990, pp. 77-87
21. [Soh01] Sohr, H.: The Navier-Stokes Equations. Basel: Birkhäuser Verlag, 2001
22. [Tay97] Taylor, M.E.: Partial Differential Equations. I-III. New York: Springer-Verlag, 1996-1997
23. [Zua02] Zuazua, E.: Controllability of partial differential equations and its semi-discrete approximations. Discrete Contin. Dyn. Syst. 8(2), 469-513 (2002)