Speaker: Nicolas Dirr, Cardiff University

Title: Stochastic Partial Differential Equations of Fluctuating Hydrodynamics.

Abstract: Stochastic Partial Differential Equations and interacting particle systems are both meant to model the same physical reality, i.e., a deterministic evolution subject to stochastic fluctuations. Conservation of mass leads typically to nonlinear noise in divergence form. These equations have no solution for white noise, i.e., for randomness on all scales. The particles, however, have a natural cut-off on small scales: The particle size. This indicates that the SPDE is a useful approximation of the particle system at intermediate scales much larger than the particle size but smaller than the macroscopic scale. On these scales, regularized noise is a natural choice. This talk gives an overview of some solution concepts, the type of noise, and some numerical results. The focus will be on equations of porous medium type and Dean-Kawasaki type.