  We study the relativistic Euler equations on the Minkowski spacetime
background. We make assumptions on the equation of state and the initial data
that are relativistic analogs of the well-known physical vacuum boundary
condition, which has played an important role in prior work on the
non-relativistic compressible Euler equations. Our main result is the
derivation, relative to Lagrangian (also known as co-moving) coordinates, of
local-in-time a priori estimates for the solution. The solution features a
fluid-vacuum boundary, transported by the fluid four-velocity, along which the
hyperbolicity of the equations degenerates. In this context, the relativistic
Euler equations are equivalent to a degenerate quasilinear hyperbolic
wave-map-like system that cannot be treated using standard energy methods.
