Navier-Stokes equations: Controllability by means of low modes forcing

Journal of Mathematical Fluid Mechanics

Volumn 7, Issue 1, 2005, Pages 108-152

  Agrachev, Andrey A ^a,b   Sarychev, Andrey V ^c  

^a SISSA   (Italy)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Controllability; Geometric control; Navier Stokes equation

Indexed keywords

ALGEBRA; APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONTROLLABILITY; GALERKIN METHODS; METRIC SYSTEM; PARTIAL DIFFERENTIAL EQUATIONS; THEOREM PROVING; TOPOLOGY;

2D NAVIER-STOKES (NS) SYSTEMS; EULER SYSTEMS; GEOMETRIC CONTROL; PIECEWISE-CONTINUOUS;

NAVIER STOKES EQUATIONS;

COMPUTATIONAL FLUID DYNAMICS; FLUID MECHANICS; MATHEMATICAL ANALYSIS; NAVIER-STOKES EQUATIONS;

EID: 15944401206     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-004-0110-1     Document Type: Article

References (17)

1. A. A. AGRACHEV AND R. V. GAMKRELIDZE, Exponential representation of flows and chronological calculus, Math. USSR Sbornik 35 (1979), 727-785.
2. A. A. AGRACHEV AND YU. L. SACHKOV, Lectures on Geometric Control Theory, SISSA, Trieste, 2001.
3. A. A. AGRACHEV AND A. V. SARYCHEV, On reduction of smooth control system, Math. USSR Sbornik 58 (1987), 15-30.
4. A. A. AGRACHEV AND A. V. SARYCHEV, Navier-Stokes Equation Controlled by Degenerate Forcing: Controllability of Finite-Dimensional Approximations, in: Proc. of Intern. Conf. Physics and Control 2003, S. Petersburg, Russia, August 20-22, 2003, 1346-1351 (CD ROM).
5. A. V. BABIN AND M. I. VISHIK, Attractors of Evolution Equations, North Holland, 1992.
6. P. CONSTANTIN AND C. FOIAS, Navier-Stokes equations, The University of Chicago Press, 1989.
7. J.-M. CORON, Return method: some applications to flow control, in: Mathematical Control Theory, ICTP Lecture Notes Series Volume VIII, Parts 1 & 2, 2002.
8. W. E AND J. C. MATTINGLY, Ergodicity for the Navier-Stokes Equation with Degenerate Random Forcing: Finite Dimensional approximation, Comm. Pure Appl. Math. 54 (2001), 1386-1402.
9. A. V. FURSIKOV, Optimal Control of Distributed Systems. Theory and Applications, AMS, Providence, 2000.
10. A. V. FURSIKOV AND O. YU. IMANUILOV, Exact controllability of the Navier-Stokes and Boussinesq equations, Russian Mathematical Surveys 54 (1999), 565-618.
11. G. GALLAVOTTI, Foundations of Fluid Mechanics, Springer-Verlag, Berlin, Heidelberg, 2002.
12. R. V. GAMKRELIDZE, Principles of Optimal Control Theory, Plenum Press, New York, 1978.
13. R. V. GAMKRELIDZE, On some extremal problems in the theory of differential equations with applications to the theory of optimal control, J. Soc. Ind. Appl. Math., Ser. A: Control 3 (1965), 106-128.
14. V. JURDJEVIC, Geometric Control Theory, Cambridge University Press, 1997.
15. S. B. KUKSIN AND A. SHIRIKIAN, Ergodicity for the randomly forced 2D Navier-Stokes equations, Mathematical Physics, Analysis and Geometry 4 (2001), 147-195.
16. M. ROMITO, Ergodicity of finite-dimensional approximations of the 3D Navier-Stokes equations forced by a degenerate noise, J. Statistical Physics 114 (2004), 155-177.
17. R. WARGA, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972.