Ergodic Properties of Randomly Forced Flows

Tuesday, February 4, 2014 - 1:30pm - 2:30pm
Lind 305
Juraj Foldes (University of Minnesota, Twin Cities)
By observing a turbulent flow, one realizes that it is unpredictable and
seemingly chaotic what is caused by the sensitivity with respect to initial
data and parameters. As early as in the 19th century, it was conjectured
that turbulent flow cannot be solely described by deterministic methods,
and it was indicated that a stochastic framework should be used. On the
other hand, some statistical properties of these flows are very stable, and
the invariant measures of the corresponding stochastic equations presumably
contain the characteristics of the stable patterns posited by the basic
theories of turbulence.
In the talk, we will discuss the existence and uniqueness of
statistically invariant state for the Boussinesq system and its mixing and
ergodic properties. No previous knowledge of stochastic equations or fluid
mechanics is required.