Relativistic equations for the generalized Chapman-Enskog hierarchy

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.