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# Applied Math Seminar: Susan Friedlander (USC)

## October 24, 2022 @ 4:15 pm - 5:15 pm

Title: Kolmogorov, Onsager and a Dyadic Model for Turbulence

Abstract: We will briefly review Kolmogorov’s ( 41) theory of homogeneous turbulence

and Onsager’s ( 49 ) conjecture that in 3-dimensional turbulent flows energy

dissipation might exist even in the limit of vanishing viscosity.

Although over the past 70 years there is a vast body of literature related to this subject,

at present there is no rigorous mathematical proof that the 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 dyadic model for turbulent energy cascades.

We will describe how results can be used to prove this dyadic model is consistent with

Kolmogorov’s theory and Onsager’s conjecture.

Aspects of the work are joint with Alexey Cheskidov, Nathan Glatt-Holtz, Roman Shvydkoy, and Vlad Vicol.