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 hypoellipitic regularity estimates, which has the ability to obtain quantitative estimates on the top Lyapunov exponents of high-dimensional, weakly dissipative SDEs.

Il seminario si terrà in presenza. Per chi volesse partecipare si prega di scrivere a classi@sns.it entro Mercoledì 13 luglio 2022 alle ore 11:00