论文标题
通过线性测试的3D Navier-Stokes系统的近似可控性证明
A proof of approximate controllability of the 3D Navier-Stokes system via a linear test
论文作者
论文摘要
我们考虑由加性有限维控制力驱动的3D Navier-Stokes系统。本文的目的是展示该系统的近似可控性如何从围绕某些合适轨迹线性的Euler系统的近似可控性得出。此处提供的证明比以前通过Lie代数方法获得的证据要短，并提供了有关控制结构的一些新信息。该方法提供的控制空间的尺寸更大，但相对于粘度仍然均匀。
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 linearised 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.
