Solutions of the relativistic Boltzmann equation are studied for all initial data which are periodic in the space variable and near equilibrium. An equilibrium is a relativistic Maxwellian distribution of momenta. Under appropriate conditions on the scattering kernel, this equilibrium is asymptotically stable in a variety of function spaces.
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Robert T. Glassey, Walter A. Strauss, Asymptotic Stability of the Relativistic Maxwellian. Publ. Res. Inst. Math. Sci. 29 (1993), no. 2, pp. 301–347DOI 10.2977/PRIMS/1195167275