Fursikov, A. V. Stabilization for the 3D Navier-Stokes system by feedback boundary control. (English) Zbl 1174.93675 Discrete Contin. Dyn. Syst. 10, No. 1-2, 289-314 (2004). 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. Cited in 54 Documents 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 Citations:Zbl 1019.93047; Zbl 0983.93021 PDFBibTeX XMLCite \textit{A. V. Fursikov}, Discrete Contin. Dyn. Syst. 10, No. 1--2, 289--314 (2004; Zbl 1174.93675) Full Text: DOI