Lagrangian Navier-Stokes diffusions on manifolds: Variational principle and stability
Lagrangian Navier-Stokes diffusions on manifolds: Variational principle and stability
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DOI：
10.1016/j.bulsci.2012.06.007
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发表时间：
2012-12-01
影响因子：
1.3
通讯作者：
Cruzeiro, Ana Bela
中科院分区：
文献类型：
--
作者：
Arnaudon, Marc;Cruzeiro, Ana Bela
证明了流形上随机流的一个变分原理。它扩展了V.I. Arnold描述的拉格朗日欧拉流，这是测地线的L-2度量的流形上，随机的情况下。本文得到了满足Navier-Stokes方程的具有平均速度（漂移）的随机拉格朗日流，并研究了这种运动轨迹的稳定性以及运动粒子之间的旋转随时间的演化。的情况下，底层的流形是二维环面进行了详细描述。(C)2012年Elsevier Masson SAS。All rights reserved.
We prove a variational principle for stochastic flows on manifolds. It extends V.I. Arnold's description of Lagrangian Euler flows, which are geodesics for the L-2 metric on the manifold, to the stochastic case. Here we obtain stochastic Lagrangian flows with mean velocity (drift) satisfying the Navier-Stokes equations.We study the stability properties of such trajectories as well as the evolution in time of the rotation between the underlying particles. The case where the underlying manifold is the two-dimensional torus is described in detail. (C) 2012 Elsevier Masson SAS. All rights reserved.