On the Cauchy problem for the relativistic Boltzmann equation in a periodic box Global existence

This paper extends the result of Hakan Andreasson. It's proved that the Cau chy problem for the relativistic Boltzmann equation in a periodic box has a global mild solution if the assumptions of the scattering cross section ar e weaker than those given by Dudynski and Ekiel-Jezewska and include some h ard relativistic interactions,and if the initial distribution function sati sfies the conditions that it's periodic in the spacial space and that its m ass,energy and. entropy are finite in the periodic box.