Grossly Determined Solutions for a Boltzmann-like Equation

TL;DR

This paper rigorously establishes a connection between kinetic gas models and continuum physics by demonstrating the existence of grossly determined solutions for a Boltzmann-like equation, bridging molecular and continuum descriptions.

Contribution

It introduces a rigorous framework for grossly determined solutions in a linear Boltzmann-like equation, linking kinetic and continuum models in gas dynamics.

Findings

Existence of grossly determined solutions for the kinetic model

Closed form balance equations derived for these solutions

Bridging molecular and continuum descriptions in gas dynamics

Abstract

In gas dynamics, the connection between the continuum physics model offered by the Navier-Stokes equations and the heat equation and the molecular model offered by the kinetic theory of gases has been understood for some time, especially through the work of Chapman and Enskog, but it has never been established rigorously. This paper established a precise bridge between this two models for a simple linear Boltzman-like equation. Specifically a special class of solutions, the grossly determined solutions, of this kinetic model are shown to exist and satisfy closed form balance equations representing a class of continuum model solutions.