Kolmogorov, Onsager and a Stochastic Model for Turbulence
November 11, 2015
3:00pm PGH 646
Abstract
We will briefly review Kolmogorov's (1941) theory of homogeneous, isotropic
turbulence and Onsager's (1949) conjecture that in 3-dimensional turbulent
flows energy dissipation might exist even in the limit of vanishing
viscosity. Although over the past 60 years there is a vast body of
literature related to this subject, at present there is no rigorous
mathematical proof that solutions to the Navier-Stokes equations yield
Kolmogorov's laws. For this reason various models have been introduced that
are more tractable but capture some of the essential features of the
Navier-Stokes equations themselves. We will discuss one such stochastically
driven dyadic model for turbulent energy cascades. We will describe how the
very recent Fields Medal results of Hairer and Mattingly for stochastic
partial differential equations can be used to prove that this dyadic model
is consistent with Kolmogorov's theory and Onsager's conjecture.
This is joint work with Nathan Glatt-Holtz and Vlad Vicol.
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Last modified: April 11 2016 - 18:14:43