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Publication 10-CNA-06

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

Peter Constantin
   Deptartment of Mathematics
University of Chicago, Chicago IL 60637
   const@math.uchicago.edu   

Gautam Iyer
   Deptartment of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA 15213
   gautam@math.cmu.edu

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 CPAM, 2008. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One notable feature of the formulation in the presence of boundaries is the non-local, implicit influence of the boundary vorticity on the interior fluid velocity.

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