The classical Boltzmann equation is a well-studied mathematical model for the evolution of rarified gases whose constituent particles have perfect spherical symmetry. As most matter in the universe that is in the gaseous phase is not made up of molecules or atoms which are perfect spheres, it is a natural question to ask how the structure of the classical Boltzmann equation changes when one modifies the geometry of the underlying gas particles.
In this talk, we present some new results on the characterisation of collision invariants for compact, strictly-convex, non-spherical particles. These results allow one to establish local conservation laws, to characterise Maxwellia, and to perform hydrodynamic limits for the analogue of the classical Boltzmann equation for non-spherical particles.
This work is in collaboration with Laure Saint-Raymond (École Normale Supérieure, Paris).