KTH/SU Mathematics Colloquium

07-10-10

Björn Birnir, UCSB

Uniqueness of solutions to the Stochastic Navier Stokes equation and Kolmogorov's Theory of Turbulence

The problem of understanding and anlyzing turbulence has occupied scientists and enginneers for at leat 500 years. Some of the most relevant observations of turbulence were made by Leonardi da Vinci and turbulence is still holding back some of the most pressing problems of modern technology. In this lecture we will discuss why it is essential to formulate the description of turbulent fluids as a noise driven process. We will explain recent result showing that the Navier-Stokes equation driven by turbulent noise has unique solutions and a unique invariant measure. This allows one to formulate a statistical theory of turbulence and prove Kolmogorov's theory of turbulence that he developed during the second world war. We will explain why these development should lead to improved numerical methods that may make possible the solution of most problems in turbulence.