GLOBAL NEWTONIAN LIMIT FOR THE RELATIVISTIC BOLTZMANN EQUATION NEAR VACUUM

We study the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data. Unique global-in-time mild solutions are obtained uniformly in the speed of light parameter c >= 1. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as c -> infinity on arbitrary time intervals [0,T], with convergence rate 1/c(2-epsilon) for any epsilon is an element of (0, 2). This may be the first proof of unique global-in-time validity of the Newtonian limit for a kinetic equation.