Hydrodynamic limit and Newtonian limit from the relativistic Boltzmann equation to the classical Euler equations

Abstract The hydrodynamic limit and Newtonian limit are important in the relativistic kinetic theory. We justify rigorously the validity of the two independent limits from the special relativistic Boltzmann equation to the classical Euler equations without assuming dependence between the Knudsen number and the light speed . This is achieved by Hilbert expansion of relativistic Boltzmann equation and the convergence rates are also obtained. New difficulties arise when tacking the uniform in and estimates for the Hilbert expansion, which have been overcome by establishing uniform‐in‐ estimates for relativistic Boltzmann operators.