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.