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Moment expansions are used as model reduction technique in kinetic gas theoryto approximate the Boltzmann equation. Rarefied gas models based on so-calledmoment equations became increasingly popular recently. However, in a seminalpaper by Holway [Phys. Fluids 7/6, (1965)] a fundamental restriction on theexistence of the expansion was used to explain sub-shock behavior of shockprofile solutions obtained by moment equations. Later, Weiss [Phys. Fluids 8/6,(1996)] argued that this restriction does not exist. We will revisit anddiscuss their findings and explain that both arguments have a correct andincorrect part. While a general convergence restriction for moment expansionsdoes exist, it cannot be attributed to sub-shock solutions. We will alsodiscuss the implications of the restriction and give some numerical evidencefor our considerations.

On the Holway-Weiss Debate: Convergence of the Grad-Moment-Expansion in Kinetic Gas Theory