Relation of exact hydrodynamics to the Chapman-Enskog series.

Abstract

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 except at the global equilibrium for an explicit example, while the exact spectrally closed hydrodynamics are defined globally for any Knudsen number. The divergence of the Chapman-Enskog series is closely related to the existence of a critical wave number for the hydrodynamic eigenvalue.