Analysis and PDE Seminar: On Universal Mixers

Friday, September 25, 2020 at 2:00pm to 3:00pm

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Andrej Zlatoš, UCSD

The problem of mixing via incompressible flows is classical and rich with connections to several branches of analysis including PDE, ergodic theory, and topological dynamics.  In this talk I will discuss some recent developments in the area and then present a construction of universal mixers - incompressible flows that asymptotically mix arbitrarily well general solutions to the corresponding transport equation - on bounded domains in all dimensions.  This mixing is in fact exponential in time (i.e., essentially optimal) for any initial condition with at least some degree of regularity, while there is no uniform mixing rate for all measurable initial conditions.

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