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

• 成果类型: Article
• 署名作者: Constantin, Peter; Iyer, Gautam
• 署名单位: University of Chicago; Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP731
• 发表日期: 2011
• 页码: 1466-1492
• 关键词: probabilistic representation; vorticity; cascades

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.