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

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.