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Stabilization for the 3D Navier-Stokes system by feedback boundary control. (English) Zbl 1174.93675

Summary: We study the problem of stabilization a solution to 3D Navier-Stokes system given in a bounded domain \(\Omega\). This stabilization is carried out with help of feedback control defined on a part \(\Gamma\) of boundary \(\partial \Omega\). We assume that \(\Gamma\) is a closed 2D manifold without boundary. Here we continue an investigation begun in [Sb. Math. 192, No. 4, 593–639 (2001); translation from Mat. Sb. 192, No. 4, 115–160 (2001; Zbl 1019.93047), J. Math. Fluid Mech. 3, No. 3, 259–301 (2001; Zbl 0983.93021)] where the stabilization problem for parabolic equation and for 2D Navier-Stokes system was studied.

MSC:

93D15 Stabilization of systems by feedback
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
37L99 Infinite-dimensional dissipative dynamical systems
76D55 Flow control and optimization for incompressible viscous fluids
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