Relativistic equations for the generalized Chapman-Enskog hierarchy

TL;DR

This paper derives a relativistic version of the Chapman-Enskog hierarchy of differential equations, incorporating a covariant time direction, which extends the classical framework to relativistic contexts.

Contribution

It introduces a covariant approach to the Chapman-Enskog hierarchy, including the Navier-Stokes system, within a relativistic framework.

Findings

Derived a relativistic version of the Chapman-Enskog hierarchy.

Introduced a covariant time direction for reduction of equations.

Extended classical differential equations to relativistic regimes.

Abstract

From the Boltzmann equation Chapman and Cowling have firstly motivated a hierarchy of differential equations. I consider a general version of these differential equations which contain the Navier-Stokes system. In the paper I derive a relativistic version of these partial differential equations. This is interesting because in the derivation a covariant version of a time direction is used. This time direction is needed to derive a reduction of the differential equations.