Non-local Korteweg stresses from kinetic theory point of view

Abstract

The aim of the paper is to elaborate a kinetic theory having the non-local Korteweg equations for non-isothermal liquid-vapour systems as the hydrodynamic limit. This is the topic of the second part of the paper. The first part of our paper is devoted to presentation of the Korteweg equations. We write the non-local Korteweg equations in a conservative form and we discuss the relations between them and the local ones.