Abstract

What do the trajectories of pollen particles suspended in water and the evolution of heat in a room have in common? These observable (macroscopic) physical phenomena are related through their microscopic dynamics. This link and its generalisations are based on standard mathematical objects from PDE and Probability theory: (fractional) diffusion equation, random walks, Brownian motion and Levy processes.

I will present a recent result concerning fractional hydrodynamical limits. Starting from a linear kinetic equation (which describes the microscopic dynamics), we derive a fractional Stokes equation governing the associated macroscopic quantities (mass, flux and temperature).

This is a joint work with Sabine Hittmeir from Technische Universitat of Vienna.

Keywords: fractional laplacian, super-diffusion, hydrodynamical limit, non-locality, Levy processes, heavy-tailed distribution, anomalous transport, scale-invariance, Stokes equation.