A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations
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.
Keywords
Cite
@article{arxiv.math/0511067,
title = {A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations},
author = {Peter Constantin and Gautam Iyer},
journal= {arXiv preprint arXiv:math/0511067},
year = {2010}
}
Comments
v4: Minor corrections to bibliography, and final version that will apear in CPAM. v3: Minor corrections to the algebra in the last section. v2: Minor changes to introduction and refferences. 14 pages, 0 figures