In this paper, we will address some recent progress on the $L^1$-stability of the Boltzmann equation near vacuum. We discuss a kinetic Glimm type interaction potential measuring the possible crossings of projected particle trajectories in physical space, and a nonlinear functional equivalent to the $L^1$-distance between two classical solutions. These functionals are employed to establish the large-time behavior and $L^1$-stability of classical solutions.

Received: 2004-11-23
Revised : 2005-04-08
Accepted: