Stabilizability of Two-Dimensional Navier—Stokes Equations with Help of a Boundary Feedback Control

By A. Fursikov. 2001

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Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system (2009, background): “6), is stated in [11,12] with X(Ω) = {y ∈ H(1)(Ω) | ∇ · y = 0, y|Γ0 = 0, tΓy · n = 0} and U(Γ) = {y ∈ H(Γ) | y|Γ0 = 0, ∫ Γ y · n = 0}, Γ = Γ∪ Γ0 and Γ∩ Γ0 = ∅.”
On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems (2014, background): “For instance, boundary feedback stabilizability of the Navier−Stokes system can be simply reduced to a uniqueness result of type [17] and avoid more sophisticate approaches for the nonstationary system as in [21,31] or [23, 24].”
Feedback boundary stabilization of the three-dimensional incompressible Navier–Stokes equations (2007, background): “For boundary controls, feedback controls are characterized in [13,14], but the corresponding laws are not pointwise in time.”