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Volume 4, Issue 3-4
Stabilization of Navier-Stokes Equations by Boundary Feedback

S. S. Ravindran

Int. J. Numer. Anal. Mod., 4 (2007), pp. 608-624.

Published online: 2007-04

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  • Abstract

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.

  • Keywords

Navier-Stokes equation, Riccati equation, stabilization, feedback control, linear quadratic regulator.

  • AMS Subject Headings

76W05, 76D55, 35B40, 35Q30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-608, author = {Ravindran , S. S.}, title = {Stabilization of Navier-Stokes Equations by Boundary Feedback}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {608--624}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/880.html} }
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 -

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.

Ravindran , S. S.. (2007). Stabilization of Navier-Stokes Equations by Boundary Feedback. International Journal of Numerical Analysis and Modeling. 4 (3-4). 608-624. doi:
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