TY - JOUR
T1 - Stabilization of Navier-Stokes Equations by Boundary Feedback
AU - Ravindran , S. S.
JO - International Journal of Numerical Analysis and Modeling
VL - 3-4
SP - 608
EP - 624
PY - 2007
DA - 2007/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/880.html
KW - Navier-Stokes equation, Riccati equation, stabilization, feedback control, linear quadratic regulator.
AB - <p style="text-align: justify;">In this paper, we consider the stabilization of steady state
solutions to Navier-Stokes equations by boundary feedback control. The
feedback control is determined by solving a linear quadratic regulator
problem associated with the linearized Navier-Stokes equations. The
control is effected through suction and blowing at the boundary. We show
that the linear feedback control provides global exponential
stabilization of the steady state solutions to the Navier-Stokes
equations for arbitrary Reynolds number. This feedback is shown to
provide global stability in both $L^2$ and $H^1$-norms.</p>