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An optimal boundary control problem for the Navier–Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H^1 / 2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in an application to viscous drag reduction.
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Gunzburger et al. (1992) studied this question.
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