Kac’s Process with Hard Potentials and a Moderate Angular Singularity

Abstract

We investigate Kac’s many-particle stochastic model of gas dynamics in the case of hard potentials with a moderate angular singularity, and show that the noncutoff particle system can be obtained as the limit of cutoff systems, with a rate independent of the number of particles N. As consequences, we obtain a wellposedness result for the corresponding Boltzmann equation and propagation of chaos in the many-particle limit $$N\rightarrow \infty $$ N → ∞ .

Propagation of chaos: A review of models, methods and applications. Ⅱ. Applications

“…The authors managed to treat the case of hard-sphere particles (unbounded cross section) but also hard-potential particles (unbounded cross section and non integrable interaction law). For similar results in the case of binary collisions, see the recent article [187]. 5.…”