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CANCELED - Kolmogorov, Onsager and a Stochastic Model for Turbulence

Thursday, March 26, 2020 - 4:30pm to 5:30pm
Location: 
WXLR A21

Speaker

Susan Friedlander
Professor and Director of Center for Applied Mathematical Sciences
Department of Mathematics
University of Southern California (USC)

Abstract

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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 60 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 stochastically driven dyadic model for turbulent energy cascades. We will describe how  results  for stochastic PDEs can be used to prove that this dyadic model is consistent with Kolmogorov’s theory and Onsager’s conjecture.

This is joint work with Vlad Vicol and Nathan Glatt-Holtz.

Bio

After many years at the University of Illinois at Chicago, Friedlander joined the University of Southern California in 2008 where she is a Professor in the Mathematics Department and Director of the Center for Applied Mathematical Sciences. Her research centers on the partial differential equations that describe the motion of fluids, namely the Euler and the Navier-Stokes equations. She is currently working in topics connected with fluid instabilities and mathematical models for turbulence. She is the Editor in Chief of the Bulletin of the American Mathematical Society. She is a fellow of the Society for Industrial and Applied Mathematics (SIAM), the American Mathematical Society (AMS), and the American Association for the Advancement of Science (AAAS), and an elected honorary member of the Moscow Mathematical Society.

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