Dear Colleagues,
the Probability research group of Pisa would like to invite you to the
following seminar by Jacob Bedrossian (University of Maryland) to be
held Wednesday, July 13th, in Aula Bianchi, at Scuola Normale Superiore in Pisa.
The seminar will take place in full presence (speaker included), but it will be streamed via Google Meets, link below.
People attending on site are kindly asked to communicate it by email at
classi@sns.it a few hours before the seminar.
Best,
F. Grotto
--------------------------------------------
Time: July 13th 2022, 14:00-15:00 CET
Speaker: Jacob Bedrossian (University of Maryland)
Title: Positive Lyapunov exponents for 2d Galerkin-Navier-Stokes with stochastic forcing
Abstract: In this talk we discuss our recent results obtaining strictly positive lower bounds on the top Lyapunov exponent of stochastic differential equations such as the weakly-damped Lorenz-96 model or Galerkin truncations of the 2d
Navier-Stokes equations (joint with Alex Blumenthal and Sam Punshon-Smith). This hallmark of chaos has long been observed in these models, however, no mathematical proof had previously been made for any type of deterministic or stochastic forcing. We propose a new method, based on the Fisher information of an associated Markov process on the sphere bundle and uniform hypoelliptic regularity estimates, which has the ability to obtain quantitative estimates on the top Lyapunov exponents of high-dimensional, weakly dissipative SDEs.