Analysis of PDE Seminar
Thursday, 09 November 2023, 02:15 pm
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Venue: Room 216, Department of Mathematics
Host: Harsha Hutridurga
Speaker: Rishabh Gvalani
Affiliation: Max Planck Institute, Leipzig.
Title: Exponential mixing by random velocity fields
Abstract: We establish exponentially fast mixing for passive scalars driven by two well-known examples of random divergence-free vector fields. The first one is the alternating shear flow model proposed by Pierrehumbert, in which case we set up a dynamics-based framework to construct such space-time smooth universal exponential mixers. The second example is the statistically stationary, homogeneous, isotropic Kraichnan model of fluid turbulence. In this case, the proof follows by a new explicit identity for the evolution of negative Sobolev norms of the scalar. This is based on joint works with Alex Blumenthal (Georgia Tech)
and Michele Coti Zelati (ICL), and Michele Coti Zelati and Theodore Drivas (Stony Brook).