SIAM Journal on Control and Optimization, Volume 59, Issue 4, Page 2411-2427, January 2021.
We consider the 3D Navier--Stokes system driven by an additive finite-dimensional control force. The purpose of this paper is to show how the approximate controllability of this system can be derived from the approximate controllability of the Euler system linearized around some suitable trajectory. The proof presented here is shorter than the previous ones obtained by Lie algebraic methods and gives some new information about the structure of the control. The dimension of the control space provided by this approach is larger, but it is still uniform with respect to the viscosity.

中文翻译：

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通过线性测试证明 3D 纳维-斯托克斯系统的近似可控性

SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2411-2427 页，2021 年 1 月。
我们考虑由附加有限维控制力驱动的 3D Navier-Stokes 系统。本文的目的是展示如何从欧拉系统围绕某个合适轨迹线性化的近似可控性推导出该系统的近似可控性。这里提出的证明比以前通过李代数方法获得的证明更短，并给出了一些关于控制结构的新信息。这种方法提供的控制空间的维度较大，但在粘度方面仍然是均匀的。