A STOCHASTIC-LAGRANGIAN APPROACH TO THE NAVIER-STOKES EQUATIONS IN DOMAINS WITH BOUNDARY

被引：33
|
作者：
Constantin, Peter [1 ]
Iyer, Gautam [2 ]
机构：
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
来源：
ANNALS OF APPLIED PROBABILITY | 2011年 / 21卷 / 04期
基金：
美国国家科学基金会;
关键词：
Navier-Stokes; stochastic Lagrangian; probabilistic representation; PROBABILISTIC REPRESENTATION; VORTICITY; CASCADES;
D O I：
10.1214/10-AAP731
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper we derive a probabilistic representation of the deterministic 3-dimensional Navier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial boundaries was done by the authors in [Comm. Pure Appl. Math. 61 (2008) 330-345]. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One aspect highlighted by the formulation in the presence of boundaries is the nonlocal, implicit influence of the boundary vorticity on the interior fluid velocity.
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页码：1466 / 1492
页数：27
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