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Beginning March 13, 2020, for the next 30 days, all events on any ASU campus or in any ASU building that are not directly related to the educational or research mission of the university are canceled in order to limit the community spread of COVID-19. Before attending a previously scheduled event on an ASU campus or in an ASU building, please check with the event organizer or look for an update online.
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.
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.
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.