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

First available: 8 August 2011

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

Navier–Stokes stochastic Lagrangian probabilistic representation


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.

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