La limite de Stokes-Fourier de l'équation de Boltzmann

Renormalized solutions of the Boltzmann equation in some appropriate scaling are shown to converge to a unique limit governed by the Stokes and heat equations as the Knudsen number vanishes. This result holds for all hard cut-off potentials and essentially the largest possible generality of scalings compatible with a formal derivation of this limit. A similar derivation of the acoustic system is obtained, however under scaling assumptions less general than predicted by the formal derivation of this limit.