Time periodic solution of the Relativistic Boltzmann Equation

The existence and stability of the time periodic solution to the relativistic Boltzmann equation around the relativistic Maxwellian in the torus are obtained. The time decay of solution to the linearized relativistic Boltzmann equation is obtained by using compensating function and basic energy estimates. By this and the contraction mapping methods the existence and stablility of time periodic solution to the relativistic Boltzmann equation are shown.