Multiple rigorous mathematical studies and kinetic theory expansions demonstrate that the Navier-Stokes equations can be formally derived from the Boltzmann equation, typically in the hydrodynamic or low Knudsen number limit.
The retrieved literature robustly confirms that the Navier-Stokes equations (and related hydrodynamic systems) can be systematically derived from the Boltzmann equation using methods such as the Chapman-Enskog expansion, Sone expansion, or rigorous hydrodynamic limits (as Knudsen numbers approach zero). While some papers discuss the physical limits or alternative expansions (such as critiques on Hilbert's sixth problem or higher-order Burnett equations), the fundamental premise that Navier-Stokes equations are derived from the Boltzmann equation is consistently supported across kinetic theory.