Dear Colleagues,
We would like to invite you to the following
SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi:
Ergodicity, Positive Lyapunov Exponents, and Partial Damping for Random Switching
by
Jonathan Mattingly (Duke University)
The seminar will take place
tomorrow TUE, 04.07.2023 at
14:00 CET in Aula Seminari, Department of Mathematics, University of Pisa and streamed online
here.
The organizers,
A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco
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Abstract: I will consider some new models inspired by the PDEs/SPDE with complex dynamics such as the 2D Euler and Navier-Stokes equations. The models introduce randomness onto the system through a random splitting scheme. I will explain how the randomly split Galerkin approximations of the 2D Euler equations and other related dynamics can be shown to possess a unique invariant measure that is absolutely continuous with respect to the natural Liouville measure, despite the existence of other invariant measures corresponding to fix points of the PDEs. I will then explain how on proves that the dynamics with respect to this measure has positive Lyapunov exponents almost surely.
Lastly, I will discuss recent results which show that the system has a unique invariant measure even when damping is applied to part of the system.
This is joint work with Omar Melikechi, Andrea Agazzi, and David Herzog.