SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2223-2246, January 2021.
In this paper, we consider an optimal control problem for the two-dimensional evolutionary Navier--Stokes system. Looking for sparsity, we take controls as functions of time taking values in a space of Borel measures. The cost functional does not involve directly the control but we assume some constraints on them. We prove the well-posedness of the control problem and derive necessary and sufficient conditions for local optimality of the controls.

中文翻译：

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二维进化纳维-斯托克斯方程的最优控制与测值控制

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2223-2246 页，2021
年1 月。在本文中，我们考虑了二维进化 Navier-Stokes 系统的最优控制问题。寻找稀疏性，我们将控件作为时间的函数，在 Borel 测度空间中取值。成本泛函不直接涉及控制，但我们假设对它们有一些约束。我们证明了控制问题的适定性，并推导出控制局部最优的充分必要条件。