Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Friday 6.7.2018 at 10:30 --- Lecture room M-223

Andrej Zlatoš (University of California San Diego):

On Universal Mixers

Abstract:

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 - 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 exists no uniform mixing rate for all measurable initial conditions.