Corrections to Fluid Dynamics

TL;DR

This paper derives a Galilean invariant fluid dynamics framework using statistical methods, resulting in a non-local basic equation that approximates to a modified Navier-Stokes system with novel features like a Dufour effect.

Contribution

It introduces a new non-local fundamental equation for fluid dynamics derived from Maxwell's balance equations, potentially replacing Boltzmann's equation.

Findings

Derived a non-local fundamental equation for fluid dynamics.

Obtained a local approximation resembling a modified Navier-Stokes system.

Identified a Dufour effect in the single-component gas model.

Abstract

We show that a Galilean invariant version of fluid dynamics can be derived by the methods of statistical dynamics using Maxwell's balance equations. The basic equation is non-local, and might replace Boltzmann's equation if the latter turns out not to have global smooth solutions in general. As an approximation, a local form of the equation of motion is derived. It turns out to be a version of the compressible Navier-Stokes system with temperature, obeying Stokes's relation, and with viscosity rising as the square-root of the temperature. The new feature is the presence of a Dufour effect for a gas of a single component.