Hilbert fluid dynamics equations expressed in Chapman-Enskog pressure tensor and heat current

TL;DR

This paper explores the detailed relationship between Chapman-Enskog and Hilbert expansions, expressing higher-order fluid dynamics equations through Chapman-Enskog's pressure tensor and heat current.

Contribution

It provides a detailed derivation connecting Hilbert and Chapman-Enskog expansions, expressing fluid equations in terms of Chapman-Enskog quantities.

Findings

Explicit expressions for Hilbert expansion fluid equations in terms of Chapman-Enskog pressure tensor and heat current.

Clarification of the connection between two fundamental kinetic theory expansions.

Enhanced understanding of higher-order fluid dynamics derivations.

Abstract

The connection between the Chapman-Enskog and Hilbert expansions is investigated in detail. In particular the fluid dynamics equations of any order in the Hilbert expansion are given in terms of the pressure tensor and heat current of the Chapman-Enskog expansion