Applied Math Seminar
Spring Quarter 2008
3:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

Friday, May 23, 2008

Bjorn Birnir
Mathematics
University of California at Santa Barbara

Turbulent Solutions of the Stochastic Navier-Stokes Equation


Abstract:

Starting with a swirling flow we prove the existence of unique turbulent solutions of the stochastically driven Navier-Stokes equation in three dimensions. These solutions are not smooth but Hölder continuous with index 1/3. The turbulent solutions give the existence of a unique invariant measure that determines the statistical theory of turbulence including Kolmogorov´s scaling laws. We will discuss how the invariant measure can be approximated leading to a implicit formula that can be used to compare with simulations and experiments.