Optimal boundary control of nonlinear-viscous fluid flows

Abstract

Abstract The optimal control problem for a stationary model of a nonlinear-viscous incompressible fluid flowing through a bounded domain is considered under the wall slip condition. As a control parameter, the dynamic pressure at the in-flow and out-flow parts of the boundary is used. Using methods of the theory of pseudomonotone mappings, the existence of a weak solution (a velocity–dynamic pressure pair) minimizing a given cost functional is proved. The behaviour of solutions and optimal values of the cost functional are studied when the set of admissible controls varies. In particular, it is shown that the marginal function of this control system is lower semicontinuous. Bibliography: 23 titles.