The small scales of the stochastic Navier-Stokes equations under rough forcing


Journal Article

© 2005 Springer Science+Business Media, Inc. We prove that the small scale structures of the stochastically forced Navier-Stokes equations approach those of the naturally associated Ornstein-Uhlenbeck process as the scales get smaller. Precisely, we prove that the rescaled kth spatial Fourier mode converges weakly on path space to an associated Ornstein-Uhlenbeck process as |k| → ∞. In addition, we prove that the Navier-Stokes equations and the naturally associated Ornstein-Uhlenbeck process induce equivalent transition densities if the viscosity is replaced with hyperviscosity. This gives a simple proof of unique ergodicity for the hyperviscous Navier-Stokes system. We show how different strengthened hyperviscosity produce varying levels of equivalence.

Full Text

Duke Authors

Cited Authors

  • Mattingly, JC; Suidan, TM

Published Date

  • January 1, 2005

Published In

Volume / Issue

  • 118 / 1-2

Start / End Page

  • 343 - 364

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-004-8787-3

Citation Source

  • Scopus