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.

中文翻译：

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非线性粘滞流体的最优边界控制

在壁滑条件下考虑了非线性黏性不可压缩流体流过有界区域的平稳模型的最优控制问题。作为控制参数，使用边界的流入和流出部分的动压力。使用伪单调映射理论的方法，证明了最小化给定成本函数的弱解（速度-动态压力对）的存在。当允许的控件集发生变化时，将研究解决方案的行为和成本函数的最佳值。特别地，表明该控制系统的边缘函数是较低的半连续的。参考书目：23种。