Speaker: Dr. Zachary Bradshaw, Department of Mathematical Sciences
Date: Wednesday, December 1, 2021, 4:05 PM – 4:55 PM
Title: Continuous data assimilation for fluid models: Foundations and new results PART-II
Abstract: Data assimilation is concerned with using coarse measurements of a system to accurately recover fine scale dynamics and has applications in engineering and forecasting. In the first part of this two-part series, we will recall the details of a novel data assimilation algorithm of Azouni, Olson and Titi for the Navier-Stokes equations. In the second part, we will discuss what goes wrong when the argument is applied on the full plane. This case is of importance because data assimilation is connected to theoretical results on turbulence by way of determining functionals. However, Kraichnan’s original theory of 2D turbulence is formulated for the plane. Hence, to use data assimilation and related arguments to affirm properties of turbulence as described by Kraichnan, elementary arguments which work for bounded domains need to be extended to the plane. Presently, it is not clear if this is possible.
Bio: Z. Bradshaw received his PhD from the University of Virginia in 2014. He then served as a post-doctoral research scholar at the University of British Columbia before returning to the University of Virginia as a visiting scholar for one year. Since 2017, he has been an assistant professor at the University of Arkansas. His research is in the Analysis of PDEs, focusing on issues of regularity, uniqueness, stability, symmetry and synchronization in fluid models.
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