Shyam Popat (Polytechnique)

Ergodicity for the Dean–Kawasaki Equation on Bounded Domains.

In this talk, I will begin by motivating the study of the Dean–Kawaski equation from the point of view of fluctuating hydrodynamics of particle systems. I will briefly mention some of the tools used to study the well-posedness of the equation in the case that the space-time white noise is replaced by coloured noise, which will be the setting of this talk. These tools include the kinetic formulation and L^1-contraction estimates. By extending the L^1-contraction to an “L^1-supercontraction” on a weighted L^1 space, I will prove ergodicity of the Dean–Kawasaki equation. More specifically, I will prove that the law of the classical Dean–Kawasaki equation converges exponentially fast to equilibrium, while for the porous medium type Dean–Kawasaki equation, the convergence occurs at a polynomial rate. This talk is based on joint work with Dr. Zhengyan Wu, and is available at https://arxiv.org/abs/2512.12861