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Index A Abstract parabolic, 26 Accretive, 15 Algebraic multiplicity, 2 Algebraic Riccati equation, 36 Asymptotically stable, 26 B Bilinear, 7 Bochner integrable, 10 Boundary controllers, 28 Boundary stabilization, 90 Brownian motion, 231 C C 0 -semigroup, 12 Closed, 1 Closed and densely defined operator, 3 Closed-loop system, 27, 53 Coercive, 7 Complexified space, 39 Conditional expectation, 230 Continuous, 7 Control system, 27 Controlled evolution system, 66 Controlled Navier Stokes system, 93 D Dirichlet map, 29 Distribution, 3 E Eigenvalue, 1 Eigenvectors, 1 Entry, 1 subentry, 1 F {F t }-stopping time, 231 Feedback controller, 53 Feedback stabilizable, 27 Filtration, 231 Floquet exponents, 74 Floquet s transformation, 159 Fredholm map, 169 Fredholm operator, 170 Function absolutely continuous, 11 finitely-valued, 10 G γ -suboptimal solution, 238 Gâteaux differentiable, 25 Generalized eigenvector, 1 Geometric multiplicity, 1 Growth logarithmic property, 14 H H -control problem, 238 Hamiltonian system, 77 High-gain Riccati-based feedback, 54 I Internal controller, 89 Internal controllers, 28 Invariant manifold, 255 Ito s formula, 49, 234 L Lax Milgram lemma, 7 Local martingale, 231 Low-gain Riccati-based feedback, 54 V. Barbu, Stabilization of Navier Stokes Flows, Communications and Control Engineering, DOI 10.1007/978-0-85729-043-4, Springer-Verlag London Limited 2011 275
276 Index M m-accretive, 15 Martingale, 230 P Periodic solution, 67 Poincaré inequality, 6 R Regular value, 169 Residual, 168 Riccati equation, 75 S Semigroup of class C 0,12 Semilinear parabolic equation, 81 Semimartingale, 231 Semisimple, 2 Sobolev embedding theorem, 5 Sobolev space, 3 Stabilizable controller, 27 Stabilizable feedback controller, 53 Stabilization problem, 27 Stochastic feedback controller, 50 Stokes operator, 18 Stokes Oseen operator, 89, 118, 168 Strong solution, 19 Strongly measurable, 10 Submartingale, 230 Supermartingale, 230 Support, 3 T Trace, 5 Transversality theorem, 169 V Variational solution, 8 W Weak, 8 Weak solution, 18 White noise, 232 Wiener process, 231 Y Yosida approximation, 15