Global Well-posedness of the Relativistic Boltzmann Equation with Large Amplitude Initial Data

Yong Wang

Published 2016-04-09Version 1

In this paper, we consider the global well-posedness of the special relativistic Boltzmann equation with large amplitude initial data. We proved the global existence and uniqueness of mild solutions to the relativistic Boltzmann equation in both whole space and torus for a class of initial data with bounded velocity-weighted $L^\infty$-norm under some additional smallness conditions on $L^1_xL^\infty_p$-norm, as well as defect mass, energy and entropy. It is noted that such initial datum are allowed to have large amplitude oscillations. Moreover, the asymptotic stability of the solutions is also investigated in the case of torus.