Advances in Differential Equations

A variational approach for optimal control of the Navier-Stokes Equations

Mathieu Colin and Pierre Fabrie

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Abstract

In this paper, we deal with optimal boundary control for the Navier-Stokes problem. We establish the existence of such a control in appropriate functional spaces. Then we study a stabilization problem around a steady state. In view of numerical approximation, we derive rigorously Euler equations satisfied by the control.

Article information

Source
Adv. Differential Equations Volume 15, Number 9/10 (2010), 829-852.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854613

Mathematical Reviews number (MathSciNet)
MR2677421

Zentralblatt MATH identifier
05794139

Subjects
Primary: 76D05: Navier-Stokes equations [See also 35Q30] 76D55: Flow control and optimization [See also 49Q10, 93C20, 93C95] 49J20: Optimal control problems involving partial differential equations 49N05: Linear optimal control problems [See also 93C05]

Citation

Colin, Mathieu; Fabrie, Pierre. A variational approach for optimal control of the Navier-Stokes Equations. Adv. Differential Equations 15 (2010), no. 9/10, 829--852. https://projecteuclid.org/euclid.ade/1355854613.


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