Speaker: Professor Sir Martin Hairer

Date: 10:00-11:00, 25th August 2025

Place: Lecture hall – K1 Building

Abstract: We show that, for a class of random velocity fields that cover solutions to the stochastic Navier-Stokes equations, the Eulerian Lyapunov exponent for passive scalar advection/diffusion is finite. This gives in particular a lower bound of order \kappa^2 on the Batchelor scale, complementing the (conjecturally sharp) upper bound of order \sqrt{\kappa} recently obtained by Bedrossian, Blumenthal, and Punshon-Smith. The proof relies on constructive bounds on the projective process that allow us to keep track of its dependence on the diffusion coefficient.