On the structure of the Chapman-Enskog expansion

We analyse the classical Chapman-Enskog expansion for the Boltzmann equation. We show that this expansion should be considered as an intermediate step in constructing the asymptotics of solutions to the Boltzmann equation for small Knudsen numbers. It is explained that the way of transformation of the expansion is quite clear for the linearized case. Difficulties of the nonlinear problem are also briefly discussed.