The Newtonian limit of the relativistic Boltzmann equation

Details The Newtonian limit of the relativistic Boltzmann equation The Newtonian limit of the relativistic Boltzmann equation

2004-04-19

arxiv.org/abs/math-ph/0404043v2

J. Math. Phys. 45 (2004), 4042-4052

Physics

Mathematical Physics

12 pages

Scientific paper

10.1063/1.1793328

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 $c\to +\infty$ the solutions converge, in a suitable norm, to the solutions of the non-relativistic Boltzmann equation for hard spheres.

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