Quantitative uniform in time hydrodynamic limits

The talk concerns the problem of hydrodynamic limits, where one tries to obtain a macroscopic PDE description from a microscopic discrete stochastic model. We review some results that have been obtained previously and present a new method that allows us to obtain uniform in time estimates on the rate of convergence. This approach is based on comparing the semigroups of the micro- and macroscopic processes via a Duhamel-type formula. Furthermore we present some results on the convergence of the microscopic entropy towards the macroscopic one.

This is joint work with Clement Mouhot.