Validity of the Boltzmann equation: how to incorporate long-range effects into a collisional dynamics

After the paper of Lanford in 1975, the short time rigorous derivation of the Boltzmann equation from a system of N particles interacting through a hard-core potential has been fully understood. In recent years, the validity of the Boltzmann equation for short-range interaction potentials has been addressed, while the long-range case is still an open problem. In this talk we will review the known results on the validity of the Boltzmann equation and discuss the instability arising from taking into account the long-range effects in the collisional dynamics by presenting a new approach to this problem.