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

Peter Constantin, Gautam Iyer

Research output: Contribution to journalArticle

64 Scopus citations

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 languageEnglish (US)
Pages (from-to)330-345
Number of pages16
JournalCommunications on Pure and Applied Mathematics
Volume61
Issue number3
DOIs
StatePublished - Mar 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A stochastic Lagrangian representation of the three-dimensional incompressible Navier-Stokes equations'. Together they form a unique fingerprint.

  • Cite this