  We prove a priori estimates for the three-dimensional compressible Euler
equations with moving {\it physical} vacuum boundary, with an equation of state
given by $p(\rho) = C_\gamma \rho^\gamma $ for $\gamma >1$. The vacuum
condition necessitates the vanishing of the pressure, and hence density, on the
dynamic boundary, which creates a degenerate and characteristic hyperbolic {\it
free-boundary} system to which standard methods of symmetrizable hyperbolic
equations cannot be applied.
