Samir Salem (Université de Toulouse)

Propagation of chaos for the Boltzmann equation with soft potentials

vendredi 27 mars 2020, 9h30

Salle du conseil, espace Turing


This talk deals with the derivation of the space homogeneous Boltzmann equation in dimension 3, from a Kac-like interacting particles system. The collision kernel is of the form $B(z,\cos(\theta)) =|z|^\gamma b(\cos(\theta))$ with $\sin(\theta)b(\cos(\theta))\sim\theta^{-1-\nu}$ for $\gamma\in (-2,0)$ and $\nu\in(0,2)$ satisfying $\gamma+\nu>0$. The result is obtained by a compacity argument, and the convergence result is given without rate, as in the work by Fournier and Hauray concerning the Landau equation.