# A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales

Source: [A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales](<https://www.sota2.com/research/paper/68fa4bf71e209131ce949b1b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-02-25T05:00:07.533Z

Authors: Zhaoli Guo, Kun Xu, Yajun Zhu

Published: 2025-08-10T05:35:51.000Z

## Abstract

Neither molecular kinetics nor continuum fluid dynamics alone is adequate to describe multiscale gas flows across different regimes. Bridging these regimes within a single self-consistent framework has long been a central challenge in fluid mechanics. We propose a unified gas kinetic framework that classifies molecules by their collision histories over an observation timescale. This formulation recovers the Boltzmann and Navier-Stokes equations as limiting cases, providing a transparent connection between kinetic and hydrodynamic descriptions. Beyond practical advantages for multiscale modeling, this framework offers a new perspective on Hilbert's sixth problem by linking microscopic dynamics to continuum mechanics through a tunable observational scale.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2508.07189>)

[PDF](<https://arxiv.org/pdf/2508.07189.pdf>)