Exponential mixing by shear flows

CDSNS Colloquium
Friday, September 2, 2022 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006; Zoom streaming available
Bill Cooperman – University of Chicago – billc@uchicago.eduhttps://math.uchicago.edu/~billc/
Alex Blumenthal

Please Note: Zoom link: https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

Given a divergence-free vector field on the torus, we consider the mixing properties of the associated flow. There is a rich body of work studying the dependence of the mixing scale on various norms of the vector field. We will discuss some interesting examples of vector fields that mix at the optimal rate, and an improved bound on the mixing scale under the extra assumption that the vector field is a shear at each time.