  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.
