A Note on Non-Hydrodynamic Solutions of Kinetic Systems

TL;DR

This paper demonstrates that certain kinetic systems have solutions that defy traditional hydrodynamic limits, revealing a spectral manifold of non-hydrodynamic solutions in phase space.

Contribution

It identifies non-hydrodynamic solutions in a kinetic system that do not conform to Chapman--Enskog scaling, highlighting new spectral phenomena.

Findings

Existence of solutions violating classical hydrodynamic scaling.

Non-convergence to Euler and Navier--Stokes equations as Knudsen number approaches zero.

Identification of a fast spectral manifold in kinetic phase space.

Abstract

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.