  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.
