The small scales of the stochastic Navier-Stokes equations under rough forcing
Publication
, Journal Article
Mattingly, JC; Suidan, TM
Published in: Journal of Statistical Physics
January 1, 2005
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.
Duke Scholars
Published In
Journal of Statistical Physics
DOI
ISSN
0022-4715
Publication Date
January 1, 2005
Volume
118
Issue
1-2
Start / End Page
343 / 364
Related Subject Headings
- Fluids & Plasmas
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences
Citation
APA
Chicago
ICMJE
MLA
NLM
Mattingly, J. C., & Suidan, T. M. (2005). The small scales of the stochastic Navier-Stokes equations under rough forcing. Journal of Statistical Physics, 118(1–2), 343–364. https://doi.org/10.1007/s10955-004-8787-3
Mattingly, J. C., and T. M. Suidan. “The small scales of the stochastic Navier-Stokes equations under rough forcing.” Journal of Statistical Physics 118, no. 1–2 (January 1, 2005): 343–64. https://doi.org/10.1007/s10955-004-8787-3.
Mattingly JC, Suidan TM. The small scales of the stochastic Navier-Stokes equations under rough forcing. Journal of Statistical Physics. 2005 Jan 1;118(1–2):343–64.
Mattingly, J. C., and T. M. Suidan. “The small scales of the stochastic Navier-Stokes equations under rough forcing.” Journal of Statistical Physics, vol. 118, no. 1–2, Jan. 2005, pp. 343–64. Scopus, doi:10.1007/s10955-004-8787-3.
Mattingly JC, Suidan TM. The small scales of the stochastic Navier-Stokes equations under rough forcing. Journal of Statistical Physics. 2005 Jan 1;118(1–2):343–364.
Published In
Journal of Statistical Physics
DOI
ISSN
0022-4715
Publication Date
January 1, 2005
Volume
118
Issue
1-2
Start / End Page
343 / 364
Related Subject Headings
- Fluids & Plasmas
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences