Tommaso Rosati (Warwick): Lower bounds to Lyapunov exponents of stochastic PDEs

When

3 – 4 p.m., May 7, 2025

We prove lower bounds to the energy dissipation rate (Lyapunov exponent) of advection-diffusion equations driven by a stochastic velocity fields, as well as for the linearisation of stochastic Navier-Stokes. This provides a first quantitative lower bound to the conjectured Batchelor scale. The proof is based on the study of spectral median dynamics, and suitable stochastic estimates.
Joint work with M. Hairer, S. Punshon-Smith and J. Yi