From the Kinetic Theory of Gases to Continuum Mechanics

TL;DR

This paper reviews recent advances in deriving continuum fluid dynamics equations from the Boltzmann equation, focusing on regimes where the fluid behaves incompressibly with constant density, using the DiPerna-Lions theory.

Contribution

It provides a comprehensive review of the kinetic-to-continuum limit results for the Boltzmann equation emphasizing the incompressible fluid regime.

Findings

Validation of the fluid dynamic limit in specific regimes

Emphasis on the incompressible flow behavior

Application of DiPerna-Lions theory to kinetic limits

Abstract

Recent results on the fluid dynamic limits of the Boltzmann equation based on the DiPerna-Lions theory of renormalized solutions are reviewed in this paper, with an emphasis on regimes where the velocity field behaves to leading order like that of an incompressible fluid with constant density.