Global Existence Proof for Relativistic Boltzmann Equation with Hard Interactions

Details Global Existence Proof for Relativistic Boltzmann Equation with Hard Interactions Global Existence Proof for Relativistic Boltzmann Equation with Hard Interactions

2009-01-04

arxiv.org/abs/0901.0372v1

Journal of Statistical Physics, Vol 130, 2008, p535-544

Physics

Mathematical Physics

Scientific paper

10.1007/s10955-007-9453-3

By combining the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation and the Dudy\'{n}ski and Ekiel-Je\.{z}ewska device of the causality of the relativistic Boltzmann equation, it is shown that there exists a global mild solution to the Cauchy problem for the relativistic Boltzmann equation with the assumptions of the relativistic scattering cross section including some relativistic hard interactions and the initial data satisfying finite mass, energy and entropy. This is in fact an extension of the result of Dudy\'{n}ski and Ekiel-Je\.{z}ewska to the case of the relativistic Boltzmann equation with hard interactions.

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