On the Boltzmann equation for rigid spheres

A formal deduction of the Boltzmann equation from the Liouville equation is presented for the case of rigid spheres. The main result is that, in the Boltzmann limit (number of molecules tending to infinity, diameter tending to zero, finite mean free path), the Boltzmann equation follows under the assumptions of a sufficiently smooth N-particle distribution function for a smooth limit to exist and of an initial datum which satisfies (at least for N → ∞) the chaos assumption. Possible extensions to molecules interacting with central forces and to dense gases are briefly discussed.