From the Boltzmann equation to fluid mechanics on a manifold

TL;DR

This paper derives fluid dynamic equations on arbitrary surfaces from the Boltzmann equation using the Chapman-Enskog method, extending kinetic theory to curved geometries.

Contribution

It introduces a novel approach to obtain hydrodynamic equations on manifolds directly from kinetic theory, generalizing classical fluid mechanics.

Findings

Hydrodynamic equations are successfully derived on arbitrary surfaces.

The method extends kinetic theory to curved geometries.

Potential applications in physics and engineering are discussed.

Abstract

We apply the Chapman-Enskog procedure to derive hydrodynamic equations on an arbitrary surface from the Boltzmann equation on the surface.