We consider the controllability of a class of systems of n Stokes equations, coupled through terms of order zero and controlled by m distributed controls. Our main result states that such a system is null-controllable if and only if a Kalman type condition is satisfied. This generalizes the case of finite-dimensional systems and the case of systems of coupled linear heat equations. The proof of the main result relies on the use of the Kalman operator introduced in [1] and on a Carleman estimate for a cascade type system of Stokes equations. Using a fixed-point argument, we also obtain that if the Kalman condition is verified, then the corresponding system of Navier–Stokes equations is locally null-controllable.

我们考虑一类n斯托克斯方程系统的可控性，通过零阶项耦合并由m分布式控制控制。我们的主要结果表明，当且仅当满足卡尔曼类型条件时，这样的系统才是空可控的。这概括了有限维系统的情况和耦合线性热方程系统的情况。主要结果的证明依赖于[1]中引入的卡尔曼算子的使用以及斯托克斯方程级联型系统的卡尔曼估计。使用定点参数，我们还得出，如果卡尔曼条件得到验证，则相应的纳维-斯托克斯方程组是局部零可控的。