  We study the evolution of a compressible fluid surrounded by vacuum and
introduce a new symmetrization in Lagrangian coordinates that allows us to
encompass both relativistic and non-relativistic fluid flows. The problem under
consideration is a free boundary problem of central interest in compressible
fluid dynamics and, from the mathematical standpoint, the main challenge to be
overcome lies in the loss of regularity in the fluid variables near the free
boundary. Based on our Lagrangian formulation, we establish the necessary a
priori estimates in weighted Sobolev spaces which are adapted to this loss of
regularity.
