Advances in Differential Equations

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

Mathieu Colin and Pierre Fabrie

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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.

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