Approximate controllability of Lagrangian trajectories of the 3D Navier–Stokes system by a finite-dimensional force
Approximate controllability of Lagrangian trajectories of the 3D Navier–Stokes system by a finite-dimensional force
复制标题
有限维力对 3D 纳维-斯托克斯系统拉格朗日轨迹的近似可控性
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
V. Nersesyan
中科院分区：
文献类型：
--
作者：
V. Nersesyan
在欧拉方法中，不可压缩流体的运动通常由Navier-Stokes系统给出的速度场来描述。速度场在保体积的超同态空间中产生一个流。后者在流体的拉格朗日描述中起着核心作用，因为它允许识别单个粒子的轨迹。在本文中，我们表明，速度场的流体和相应的流动的同构可以同时近似控制使用有限维外力。证明是基于一些方法从几何控制理论介绍了Agrachev和Sarychev。
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier–Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms. The latter plays a central role in the Lagrangian description of a fluid, since it allows to identify the trajectories of the individual particles. In this paper, we show that the velocity field of the fluid and the corresponding flow of diffeomorphisms can be simultaneously approximately controlled using a finite-dimensional external force. The proof is based on some methods from the geometric control theory introduced by Agrachev and Sarychev.