Modul: MAT070 Zurich Colloquium in Mathematics

## On the dynamics of dilute gases

Talk by Prof. Dr. Isabelle Gallagher

**Date:** 26.03.24 **Time:** 16.30 - 18.00 **Room:**

The evolution of a gas can be described by different models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. On the one hand Lanford showed in 1974 that the Boltzmann equation appears as a law of large numbers in the low density limit of a gas of hard spheres, at least for very short times. On the other hand, fluid mechanics equations such as the Navier-Stokes equations can be derived from the Boltzmann equation in the limit of when the mean free path tends to zero. Reconciling both approaches in order to derive fluid mechanics equations from Newton's laws for the system of particles is to this day an open question.

In this talk we shall explain these different limiting procedures, their difficulties and some recent advances in Hilbert's program.