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Stabilization of Navier–Stokes Flows

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Stabilization of Navier–Stokes Flows

Part of the book series: Communications and Control Engineering ((CCE))

Abstract

In this chapter we discuss the feedback stabilization of stationary (equilibrium) solutions to Navier–Stokes equations. The design of a robust stabilizing feedback control is the principal way to suppress instabilities and turbulence occurring in the dynamics of the fluid and we treat this problem in the case of internal and boundary controllers. The first case, already presented in an abstract setting in Chap. 2, is that in which the controller is distributed in a spatial domain \(O\) and has compact support taken arbitrarily small. The second case is that where the controller is concentrated on the boundary \(\partial O\). In both cases, we design a stabilizable feedback linear controller which is robust and has a finite-dimensional structure, that is, it is a linear combination of eigenfunctions for the corresponding linearized systems. From the control theory point of view, this means that the actuation, though infinite-dimensional, is confined to an arbitrary subdomain \(O_{\rm 0} \) or to the boundary.

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Authors and Affiliations

  1. Fac. Mathematics, Al. I. Cuza University, Blvd. Carol I 11, 700506, Iaşi, Romania

    Prof. Viorel Barbu

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  1. Prof. Viorel Barbu
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Correspondence to Viorel Barbu .

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© 2011 Springer-Verlag London Limited

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Barbu, V. (2011). Stabilization of Navier–Stokes Flows. In: Stabilization of Navier–Stokes Flows. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-043-4_3

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  • DOI: https://doi.org/10.1007/978-0-85729-043-4_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-042-7

  • Online ISBN: 978-0-85729-043-4

  • eBook Packages: EngineeringEngineering (R0)

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