The Small Scales of the Stochastic Navier Stokes Equations under Rough Forcing

Details The Small Scales of the Stochastic Navier Stokes Equations under Rough Forcing The Small Scales of the Stochastic Navier Stokes Equations under Rough Forcing

2004-08-30

arxiv.org/abs/math-ph/0408060v1

Physics

Mathematical Physics

Accepted for publication by the Journal of Statistical Physics

Scientific paper

10.1007/s10955-004-8787-3

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 k-th spatial Fourier mode converges weakly on path space to an associated Ornstein-Uhlenbeck process as |k| --> infty . 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 sufficient 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.

Affiliated with

Also associated with

No associations

Rating

The Small Scales of the Stochastic Navier Stokes Equations under Rough Forcing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Small Scales of the Stochastic Navier Stokes Equations under Rough Forcing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Small Scales of the Stochastic Navier Stokes Equations under Rough Forcing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-689603