Global existence and asymptotic stability near equilibrium for the relativistic BGK model

In this paper, the relativistic BGK model is studied. The Jüttner function is presented as the relativistic counterpart of the local Maxwellian equilibrium in the classical case. By linearization around this equilibrium, we obtain a linearized relativistic BGK model and study their time decay at infinity. Finally, existence and asymptotic behavior of close-to-equilibrium solutions of the whole nonlinear relativistic BGK model are proved.