Return to Colloquia & Seminar listing
Uniqueness of Solutions to the Stochastic Navier-Stokes, the Invariant Measure and Kolmogorov's Theory.
PDE & Applied Mathematics| Speaker: | Björn Birnir, University of California at Santa Barbara |
| Location: | 3106 MSB |
| Start time: | Wed, Feb 13 2008, 11:00AM |
Description
The existence and uniqueness of solutions of the Stochastic
Navier-Stokes equation driven
with additive noise in three dimensions is proven, in the presence of
uni-directional mean flow and some swirl. The existence of a unique
invariant measure is established and the properties of this measure
are described. The invariant measure is used to prove Kolmogorov's
scaling in 3-dimensional turbulence including the celebrated $-5/3$
power law for the decay of the power spectrum of a turbulent
3-dimensional flow.