  In this paper, we prove a new type of energy estimates for the compressible
Euler's equation with free boundary, with a boundary part and an interior part.
These can be thought of as a generalization of the energies in Christodoulou
and Lindblad [CL] to the compressible case and do not require the fluid to be
irrotational. In addition, we show that our estimates are in fact uniform in
the sound speed. As a consequence, we obtain convergence of solutions of
compressible Euler equations with a free boundary to solutions of the
incompressible equations, generalizing the result of Ebin [Eb] to when you have
a free boundary. In the incompressible case our energies reduces to those in
[CL] and our proof in particular gives a simplified proof of the estimates in
[CL] with improved error estimates. Since for an incompressible irrotational
liquid with free surface there are small data global existence results our
result leaves open the possibility of long time existence also for slightly
compressible liquids with a free surface.
