Global Well-posedness of the Relativistic Boltzmann Equation

Abstract

In this paper, we prove the global existence and uniqueness of mild solution to the relativistic Boltzmann equation both in the whole space and in torus for a class of initial data with bounded velocity-weighted $L^\infty$-norm and some smallness on $L^1_xL^\infty_p$-norm as well as on defect mass, energy and entropy. Moreover, the asymptotic stability of the solutions is also investigated in the case of torus.