This work is concerned about some distributed optimal control problems governed by two-dimensional convective Brinkman–Forchheimer (CBF) equations, which describe the motion of incompressible viscous fluid through a rigid, homogeneous, isotropic, porous medium. We address a distributed optimal control problem of minimizing a suitable cost functional subjected to 2D CBF equations with state constraints. We establish the existence of an optimal solution and obtain the first-order necessary conditions of optimality for such optimal control problems.

中文翻译：

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带状态约束的二维对流Brinkman-Forchheimer方程最优控制的一阶必要条件

这项工作关注一些由二维对流 Brinkman-Forchheimer (CBF) 方程控制的分布式最优控制问题，这些方程描述了不可压缩粘性流体在刚性、均匀、各向同性、多孔介质中的运动。我们解决了一个分布式最优控制问题，即最小化受具有状态约束的 2D CBF 方程约束的合适成本函数。我们建立了最优解的存在性，并获得了此类最优控制问题最优性的一阶必要条件。