On Phase Boundaries in Relativistic Korteweg Fluids

TL;DR

This paper extends Lorentz-invariant Korteweg theory to study phase boundaries in relativistic fluids, establishing the existence of regular phase fronts in the Euler-Korteweg equations within a relativistic framework.

Contribution

It introduces a Lorentz-invariant formulation of Korteweg's capillarity theory and demonstrates the existence of phase fronts with heteroclinic profiles in relativistic Euler equations.

Findings

Established a family of phase fronts with heteroclinic profiles.

Extended classical Korteweg theory to a relativistic context.

Lays groundwork for further studies on phase boundaries in relativistic fluids.

Abstract

This is the first of several planned papers that study the existence and local-in-time persistence of phase fronts in the Lorentz invariant Euler equations for gases of van der Waals type, aiming at transferring earlier results of Slemrod and of Benzoni-Gavage and collaborators to the context of the theory of relativity. While the later papers will examine more general admissibility criteria, this one uses and extends the author's Lorentz invariant formulation of Korteweg's theory of capillarity, establishing a family of phase fronts that have a regular heteroclinic profile with respect to the associated Euler-Korteweg equations.