  We study the problem of inviscid slightly compressible fluids in a bounded
domain. We find a unique solution to the initial-boundary value problem and
show that it is near the analogous solution for an incompressible fluid
provided the initial conditions for the two problems are close. In particular,
the divergence of the initial velocity of the compressible flow at time zero is
assumed to be small. Furthermore we find that solutions to the compressible
motion problem in Lagrangian coordinates depend differentiably on their initial
data, an unexpected result for this type of non-linear equations.
