The Existence of Global Solutions to a Fluid Dynamic Model for Materials for Korteweg Type

Abstract

We discuss the existence of global solutions to a fluid dynamic model for materials of Korteweg type, and discuss the three dimensional nonisothermal motion. The higher order derivatives of density in the constitutive relation makes it necessary to introduce an interstitial working term in the energy equation. This makes the energy estimate more involved. Nevertheless, it is possible to show the existence of global solutions by the euergy method.