The Stokes-Fourier limit for the Boltzmann equation

Renormalized solutions of the Boltzmann equation in some appropriate scalin g are shown to converge to a unique limit governed by the Stokes and heat e quations 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 ge neral than predicted by the formal derivation of this limit. (C) 2001 Acade mic des sciences/Editions scientifiques et medicales Elsevier SAS.