The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 21, Number 4 (2011), 1466-1492.
A stochastic-Lagrangian approach to the Navier–Stokes equations in domains with boundary
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.
Ann. Appl. Probab. Volume 21, Number 4 (2011), 1466-1492.
First available in Project Euclid: 8 August 2011
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Constantin, Peter; Iyer, Gautam. A stochastic-Lagrangian approach to the Navier–Stokes equations in domains with boundary. Ann. Appl. Probab. 21 (2011), no. 4, 1466--1492. doi:10.1214/10-AAP731. http://projecteuclid.org/euclid.aoap/1312818842.