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We derive the linear acoustic and Stokes-Fourier equations as the limitingdynamics of a system of N hard spheres of diameter $\epsilon$ in two spacedimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N$\epsilon$ = $\alpha$ $\rightarrow$ $\infty$, using the linearized Boltzmannequation as an intermediate step. Our proof is based on Lanford's strategy[18], and on the pruning procedure developed in [5] to improve the convergencetime to all kinetic times with a quantitative control which allows us to reachalso hydrodynamic time scales. The main novelty here is that uniform L 2 apri-ori estimates combined with a subtle symmetry argument provide a weakversion of chaos, in the form of a cumulant expansion describing the asymptoticdecorrelation between the particles. A refined geometric analysis ofrecollisions is also required in order to discard the possibility of multiplerecollisions.

From hard sphere dynamics to the Stokes-Fourier equations: An $L^2$ analysis of the Boltzmann-Grad limit