Abstract
In this paper we derive a probabilistic representation of the deterministic three-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 Lagrangian-averaged Navier-Stokes alpha models.
Original language | English (US) |
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Pages (from-to) | 330-345 |
Number of pages | 16 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 61 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2008 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics