A Note on Non-Hydrodynamic Solutions of Kinetic Systems

We show that the one-dimensional three-component Grad system admits solutions that violate the Chapman--Enskog scaling in Knudsen number. In particular, there exist solutions that do not converge to the analogues of the Euler and Navier--Stokes equations for vanishing Knudsen number. These non-hydrodynamic solutions correspond to a fast spectral manifold in kinetic phase space.