From hard spheres dynamics to the Stokes-Fourier equations: An L² analysis of the Boltzmann-Grad limit

We derive the Stokes-Fourier equations in dimension 2 as the limiting dynamics of a system of N hard spheres of diameter ε when N→∞, ε→0, Nε=α→∞, using the linearized Boltzmann equation as an intermediate step. Our proof is based on the strategy of Lanford [6], and on the pruning procedure developed in [3] to improve the convergence time. The main novelty here is that uniform a priori estimates come from a L² bound on the initial data, the time propagation of which involves a fine symmetry argument and a systematic study of recollisions.