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

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

2010-03-12

arxiv.org/abs/1003.2461v4

Annals of Applied Probability 2011, Vol. 21, No. 4, 1466-1492

Mathematics

Analysis of PDEs

Published in at http://dx.doi.org/10.1214/10-AAP731 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP731

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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