Justification of limit for the Boltzmann equation related to Korteweg theory

Under the diffusion scaling and a scaling assumption on the microscopic component, a non-classical fluid dynamic system was derived by Bardos et al. (2008) that is related to the system of ghost effect derived by Sone (2007) in a different setting. By constructing a non-trivial solution to the limiting system that is closely related to the Korteweg theory, we prove that there exists a sequence of smooth solutions of the Boltzmann equation that converge to the limiting solution when the Knudsen number vanishes. This provides the first rigorous nonlinear derivation of Korteweg theory from the Boltzmann equation and re-emphasizes the importance of Korteweg theory for the problem of thermal creep flow.