Local null controllability of a two-dimensional fluid-structure interaction problem

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 14, Issue 1, 2008, Pages 1-42

  Boulakia, Muriel ^a   Osses, Axel ^b  

^a UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

^b UNIVERSITY OF CHILE   (Chile)

Author keywords

Carleman estimates; Controllability; Fluid solid interaction; Navier Stokes equations

Indexed keywords

CONTROLLABILITY; FLUID DYNAMICS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING; TWO DIMENSIONAL;

CARLEMAN ESTIMATES; FLUID DOMAIN; FLUID-SOLID INTERACTION; LINEARIZED SYSTEM;

FLUID STRUCTURE INTERACTION;

EID: 38149008170     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2007031     Document Type: Article

References (23)

1. S. Anita and V. Barbu, Null controllability of nonlinear convective heat equations. ESAIM: COCV 5 (2000) 157-173.
2. M. Boulakia and A. Osses, Local null controllability of a two-dimensional fluid-structure interaction problem. Prépublication 139, UVSQ (octobre 2005).
3. C. Conca, J. San Martin and M. Tucsnak, Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid. Comm. Partial Differential Equations 25 (2000) 1019-1042.
4. J.M. Coron and S. Guerrero, Singular optimal control: A linear 1-D parabolic-hyperbolic example. Asymptot. Anal. 44 (2005) 237-257.
5. B. Desjardins and M.J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Arch. Ration. Mech. Anal. 146 (1999) 59-71.
6. A. Doubova and E. Fernandez-Cara, Some control results for simplified one-dimensional models of fluid-solid interaction. Math. Models Methods Appl. Sci. 15 (2005) 783-824.
7. C. Fabre and G. Lebeau, Prolongement unique des solutions de l'équation de Stokes. Comm. Partial Diff. Equations 21 (1996) 573-596.
8. C. Fabre, J.-P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Royal Soc. Edinburgh 125A (1995) 31-61.
9. E. Fernandez-Cara and E. Zuazua, The cost of approximate controllability for heat equations: the linear case. Adv. Differential Equations 5 (2000) 465-514.
10. E. Fernandez-Cara, S. Guerrero, O. Yu. Imanuvilov and J.-P. Puel, Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. 83 (2004) 1501-1542.
11. A.V. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996).
12. O.Yu. Imanuvilov, Remarks on exact controllability for the Navier-Stokes equations. ESAIM: COCV 6 (2001) 39-72.
13. O.Yu. Imanuvilov and J.-P. Puel, Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems. Internat. Math. Res. Notices 16 (2003) 883-913.
14. O.Yu. Imanuvilov and T. Takahashi, Exact controllability of a fluid-rigid body system. Prépublication IECN (novembre 2005).
15. O. Nakoulima, Contrôlabilité à zéro avec contraintes sur le contrôle. C. R. Acad. Sci. Paris Ser. I 339 (2004) 405-410.
16. A. Osses and J.P. Puel, Approximate controllability for a linear model of fluid structure interaction. ESAIM: COCV 4 (1999) 497-513.
17. J.P. Raymond and M. Vanninathan, Exact controllability in fluid-solid structure: the Helmholtz model. ESAIM: COCV 11 (2005) 180-203.
18. J. San Martin, V. Starovoitov and M. Tucsnak, Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid. Arch. Rational Mech. Anal. 161 (2002) 113-147.
19. T. Takahashi, Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain, Adv. Differential Equations 8 (2003) 1499-1532.
20. R. Temam, Behaviour at time t = 0 of the solutions of semi-linear evolution equations. J. Diff. Equations 43 (1982) 73-92.
21. J.L. Vázquez, E. Zuazua, Large time behavior for a simplified ID model of fluid-solid interaction. Comm. Partial Differential Equations 28 (2003) 1705-1738.
22. J.L. Vázquez and E. Zuazua, Lack of collision in a simplified 1-dimensional model for fluid-solid interaction. Math. Models Methods Apll. Sci., MSAS 16 (2006) 637-678.
23. X. Zhang and E. Zuazua, Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system. J. Differential Equations 204 (2004) 380-438.