On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series

We demonstrate that the Chapman-Enskog series is locally equivalent to the exact spectral closure defined on slow kinetic eigenmodes in the limit of vanishing Knudsen number. We further show that the Chapman-Enskog series diverges everywhere expect at the global equilibrium for an explicit example, while the exact spectrally closed hydrodynamics are defined globally for any Knudsen number.