  In this paper, we give an overview of the results established in [3] which
provides the first rigorous derivation of hydrodynamic equations from the
Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a
new system of hydrodynamic equations describing granular flows and prove
existence of classical solutions to the aforementioned system. One of the main
issue is to identify the correct relation between the restitution coefficient
(which quantifies the rate of energy loss at the microscopic level) and the
Knudsen number which allows us to obtain non trivial hydrodynamic behavior. In
such a regime, we construct strong solutions to the inelastic Boltzmann
equation, near thermal equilibrium whose role is played by the so-called
homogeneous cooling state. We prove then the uniform exponential stability with
respect to the Knudsen number of such solutions, using a spectral analysis of
the linearized problem combined with technical a priori nonlinear estimates.
Finally, we prove that such solutions converge, in a specific weak sense,
towards some hydrodynamic limit that depends on time and space variables only
through macroscopic quantities that satisfy a suitable modification of the
incompressible Navier-Stokes-Fourier system.
