Some controllability results for the N-dimensional Navier-Stokes and boussinesq systems with N - 1 scalar controls

SIAM Journal on Control and Optimization

Volumn 45, Issue 1, 2006, Pages 146-173

  Fernández Cara, Enrique ^a   Guerrerq, Sergio ^a   Imanuvilov, Oleg Yu ^b   Puel, Jean Pierre ^c  

^a UNIVERSITY OF SEVILLE   (Spain)

^b IOWA STATE UNIVERSITY   (United States)

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

Author keywords

Carleman inequalities; Exact controllability; Navier Stokes system

Indexed keywords

BOUSSINESQ SYSTEMS; CARLEMAN INEQUALITIES; EXACT CONTROLLABILITY; NAVIER STOKES SYSTEMS; SCALAR CONTROL FUNCTIONS;

APPROXIMATION THEORY; FUNCTIONS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING;

LINEAR CONTROL SYSTEMS;

EID: 33847073820     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/04061965X     Document Type: Article

References (16)

1. V. M. ALEKSEEV, V. M. TIKHOMIROV, AND S. V. FOMIN, Optimal Control, Translated from the Russian by V. M. Volosov, Contemporary Soviet Mathematics, Consultants Bureau, New York, 1987.
2. J.-P. AUBIN, L'Analyse non Linéaire et ses Motivations Économiques, Masson, Paris, 1984.
3. J.-M. CORON, On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions, ESAIM Control Optim. Cale. Var., 1 (1996), pp. 35-75.
4. C. FABRE, Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems, ESAIM Control Optim. Calc. Var., 1 (1995/96), pp. 267-302.
5. C. FABRE, J.-P. FUEL, AND E. ZUAZUA, Approximate controllability of the semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), pp. 31-61.
6. E. FERNÁNDEZ-CARA AND S. GUERRERO, Global Carleman inequalities for parabolic systems and applications to controllability, SIAM J. Control Optim., to appear.
7. E. FERNÁNDEZ-CARA, S. GUERRERO, O. YU. IMANUVILOV AND J.-P. PUEL, Local exact controllability of the Navier-Stokes system, J. Math. Pures Appl., 83/12 (2004), pp. 1501-1542.
8. A. FURSIKOV AND O. YU. IMANUVILOV, Local exact controllability for 2-D Navier-Stokes equations, Sb. Math. 187, 9 (1996), pp. 1355-1390.
9. A. FURSIKOV AND O. YU. IMANUVILOV, Controllability of Evolution Equations, Lecture Notes 34, Seoul National University, Korea, 1996.
10. A. FURSIKOV AND O. YU. IMANUVILOV, Exact controllability of the Navier-Stokes and Boussinesq equations, Russian Math. Surveys, 54 (1999), pp. 565-618.
11. G. GEYMONAT AND E. SÁNCHEZ-PALENCIA, On the vanishing viscosity limit for acoustic phenomena in a bounded region, Arch. Ration. Mech. Anal., 75 (1981), pp. 257-268.
12. S. GUERRERO, Local exact controllability to the trajectories of the Boussinesq system, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.
13. O. YU. IMANUVILOV, Remarks on exact controllability for the Navier-Stokes equations, ESAIM Control Optim. Calc. Var., 6 (2001), pp. 39-72.
14. O. YU. IMANUVILOV AND J.-P. PUEL, Global Carleman estimates for weak elliptic non homogeneous Dirichlet problem, Int. Math. Res. Not., 16 (2003), pp. 883-913.
15. O. YU. IMANUVILOV AND M. YAMAMOTO, Carleman estimate for a parabolic equation in a Sobolev space of negative order and its applications, in Control of Nonlinear Distributed Parameter Systems, G. Chen, I. Lasiecka, and J. Zhou, eds., Lecture Notes in Pure and Appl. Math. 218, Dekker, New York 2001, pp. 113-137.
16. J.-L. LIONS and E. ZUAZUA, A generic uniqueness result for the Stokes system and its control theoretical consequences, Partial Differential Equations and Appl., 177 (1996), pp. 221-235.