The Chapman-Enskog procedure as a form of degenerate perturbation theory

A formal analogy between the linear Chapman-Enskog procedure and a variant of the perturbation theory of degenerate levels, as presented by C. Bloch, is established. The analogy is than exploited to obtain closed expressions for the Chapman-Enskog special solutions to all orders in the perturbation parameter and for the evolution equations of the hydrodynamic variables, that determine the asymptotic solutions of the underlying evolution equation. The analogy can also be used to express the initial values of these “asymptotic equations” in terms of the initial value of the full evolution equation.