The Newtonian limit of the relativistic Boltzmann equation

The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter c>c(0) for a properly large and positive c(0). A local existence and uniqueness theorem is proved in an interval of time independent of c>c(0) and conditions are given such that in the limit c-->+infinity the solutions converge, in a suitable norm, to the solutions of the nonrelativistic Boltzmann equation for hard spheres. (C) 2004 American Institute of Physics.