Mixing and enhanced relaxation in fluid flows

Thursday, April 15, 2010 - 11:30am - 12:15pm
EE/CS 3-180
Alexander Kiselev (University of Wisconsin, Madison)
Keywords: passive scalar, enhanced diffusion, mixing

Abstract: We consider passive scalar equation on a compact domain or manifold.
The fluid flow can aid diffusion and increase the speed of convergence of
the initial distribution to its average. We consider either stationary
or time periodic flows, and derive a sharp characterization of flows that
are particularly effective in enhancing the relaxation speed to mean value.
The characterization links enhanced relaxation with spectral properties
of the dynamical system generated by flow. The results also provide an indication that time dependence of the flow may improve relaxation enhancing properties. Methods used involve a mix of PDE techniques and functional
analysis. A key role is played by estimates similar to ones used in
quantum dynamics to measure the rate of wavepacket propagation.
The talk is based on works joint with P. Constantin, L. Ryzhik, R. Shterenberg
and A. Zlatos.
MSC Code: