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→∞ on arbitrary time intervals [0, T ], with convergence rate 1/c2− for any ∈ (0, 2). This may be the first proof of unique global-in-time validity of the Newtonian limit for a kinetic equation.