This article is concerned with the local well-posedness problem for the
compressible Euler equations in gas dynamics. For this system we consider the
free boundary problem which corresponds to a physical vacuum. Despite the clear
physical interest in this system, the prior work on this problemis limited to
Lagrangian coordinates, in high regularity spaces. Instead, the objective of
the present work is to provide a new, fully Eulerian approach to this problem,
which provides a complete, Hadamard style well-posedness theory for this
problem in low regularity Sobolev spaces. In particular we give new proofs for
both existence, uniqueness, and continuous dependence on the data with sharp,
scale invariant energy estimates, and continuation criterion.
