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.

**Basil Nicolaenko Memorial Distinguished Lecture
Thursday, March 17
4:30pm MST/AZ
Virtual via Zoom**

https://asu.zoom.us/j/84444366354?pwd=anJpYVhBMjZ2cmkwWEtwNEozeFQrZz09

The Basil Nicolaenko Memorial Distinguished Lecture Series in Nonlinear Studies was created to recognize and honor Professor Nicolaenko's exemplary career in mathematics and his passion and intellectual curiosity for teaching nonlinear studies. He was one of the co-founding members of the Center for Nonlinear Studies at the Los Alamos National Laboratory in 1980 and joined the ASU mathematics faculty in 1988 where he was a key leader in the Environmental Fluid Dynamics Group.

Susan Friedlander

Professor

USC