Boundary control problems for a stationary model of magnetohydrodynamics of a viscous incompressible fluid are considered in a domain with non-ideal boundary. The role of the control is played by a tangential component of a magnetic field specified on an entire boundary. In the case when the control function is square integrable, the solvability of the control problem is proved. Under assumption that control possesses a higher smoothness described by the space H^s(Γ)³ for any s > 0, an optimality system is derived. Based on the analysis of an optimality system, the local stability estimates of optimal solutions are established with respect to small perturbations of a cost functional.

中文翻译：

---

非理想边界域中平稳磁流体动力学方程的边界控制问题

在具有非理想边界的域中考虑了粘性不可压缩流体的磁流体动力学平稳模型的边界控制问题。控制的作用是由在整个边界上指定的磁场的切向分量发挥的。在控制函数为平方可积的情况下，证明了控制问题的可解性。假设对于任何s > 0，控制具有由空间H ^s（Γ）³描述的更高的平滑度，则可以得出最优系统。基于最优系统的分析，针对成本函数的小扰动建立了最优解的局部稳定性估计。