Tuesday, February 4, 2025 3:30pm to 4:30pm
About this Event
Title; How fast can small perturbations of viscous flows de-correlate?
Abstract: Small perturbations of bounded Navier–Stokes flows separate at most at a linear rate. In forecasting applications this can result in de-correlation of a forecast from the real-world flow after a short but fixed period of time. In weather forecasts this corresponds to a roughly five day window in which forecasts are reliably predictive. Mathematically, it is not known if solutions to the 3D Navier–Stokes equations in the natural energy class are bounded. This raises the prospect that de-correlation can occur at a faster than linear rate. This talk will summarize abstract work done in this direction with a focus on stating open problems which may benefit from computational studies.
Biosketch: Dr. Zachary Bradshaw is an associate professor in the Department of Mathematical Sciences at the University of Arkansas. He studies fluids and fluid dynamics using the tools of mathematical analysis. His recent work, which has focused on the Navier-Stokes equations, has examined how fast flows can separate, uniqueness criteria in terms of the error, eventual regularity for data with low integrability and the emergence of eddies in nonlinear stationary flows. Dr. Bradshaw received his PhD from the University of Virginia with Zoran Grujic. After that, he was a post-doc at the University of British Columbia with Tai-Peng Tsai. He has been at the University of Arkansas since 2017. While at the University of Arkansas, he was an assistant professor from 2017 to 2022.
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