  We introduce non-perturbative analytical techniques for the derivation of the
hydrodynamic manifolds from kinetic equations. The new approach is analogous to
the Schwinger-Dyson equation of quantum field theories, and its derivation is
demonstrated with the construction of the exact diffusion manifold for a model
kinetic equation. The novel approach is superior to the classical
Chapman-Enskog method.

Fluid Dynamics;Statistical Mechanics