Exact linear hydrodynamics from the Boltzmann equation

TL;DR

This paper derives exact linear hydrodynamic equations from the Boltzmann equation, demonstrating their hyperbolicity, stability, and H-theorem, thus providing a rigorous foundation for hydrodynamics at all Knudsen numbers.

Contribution

It presents the first derivation of exact linear hydrodynamics directly from the Boltzmann equation with Bhatnagar-Gross-Krook collision integral, valid to all orders in Knudsen number.

Findings

Proves the hyperbolicity of the derived equations

Establishes the stability of the hydrodynamic equations

Demonstrates the existence of an H-theorem for the system

Abstract

Exact (to all orders in Knudsen number) equations of linear hydrodynamics are derived from the Boltzmann kinetic equation with the Bhatnagar-Gross-Krook collision integral. The exact hydrodynamic equations are cast in a form which allows us to immediately prove their hyperbolicity, stability, and existence of an H-theorem.