Justification of limit for the Boltzmann equation related to Korteweg theory (Q2821878)

In this article the authors give, through a diffusion scaling, a rigorous derivation of Korteweg's theory from the Boltzmann's equation. Namely they construct diffusion waves and study the hydrodynamic limit of the rescaled Boltzmann's equation to such diffusion waves and they show that their analysis gives a rigorous derivation of Korteweg theory of capillarity.