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A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations

Peter Constantin·Gautam Iyer
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Abstract

In this paper we derive a representation of the deterministic 3-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self-contained proof of local existence for the nonlinear stochastic system, and can be extended to formulate stochastic representations of related hydrodynamic-type equations, including viscous Burgers equations and LANS-alpha models.

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Peter Constantin, Gautam Iyer. 2006-08-31. A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations. https://doi.org/10.1002/cpa.20192

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