The Annals of Applied Probability

A stochastic-Lagrangian approach to the Navier–Stokes equations in domains with boundary

Peter Constantin and Gautam Iyer

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Abstract

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.

Article information

Source
Ann. Appl. Probab. Volume 21, Number 4 (2011), 1466-1492.

Dates
First available: 8 August 2011

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1312818842

Digital Object Identifier
doi:10.1214/10-AAP731

Zentralblatt MATH identifier
05957119

Mathematical Reviews number (MathSciNet)
MR2857454

Subjects
Primary: 76D05: Navier-Stokes equations [See also 35Q30] 60K40: Other physical applications of random processes

Keywords
Navier–Stokes stochastic Lagrangian probabilistic representation

Citation

Constantin, Peter; Iyer, Gautam. A stochastic-Lagrangian approach to the Navier–Stokes equations in domains with boundary. The Annals of Applied Probability 21 (2011), no. 4, 1466--1492. doi:10.1214/10-AAP731. http://projecteuclid.org/euclid.aoap/1312818842.


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