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

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 -> infinity.

Automated summary

We investigate Kac's many-particle stochastic model of gas dynamics with hard potentials and moderate angular singularity. We show that the noncutoff particle system can be obtained as the limit of cutoff systems, regardless of the number of particles N. As a result, we establish the wellposedness of the corresponding Boltzmann equation and the propagation of chaos in the many-particle limit N -> infinity.