Hydrodynamic Limits of the Boltzmann Equation

The classical PDEs of Fluid
Mechanics (Euler and Navier-Stokes) can be formally deduced from the Boltzmann
equation of the kinetic theory of gases. Such formal derivations are based on
the asymptotic analysis of the Boltzmann equation under specific scaling assumptions.
After discussing these formal derivations, we shall describe mathematical tools
and ideas involved in the rigorous proof of such results.