The Newtonian limit of the relativistic Boltzmann equation
Abstract
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>c0 for a properly large and positive c0. A local existence and uniqueness theorem is proved in an interval of time independent of c>c0 and conditions are given such that in the limit c +∞ the solutions converge, in a suitable norm, to the solutions of the non-relativistic Boltzmann equation for hard spheres.
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