ABSTRACT We show that the motion of a slightly compressible fluid is near that of an incompressible fluid.
That is, for a given initial velocity field, the motion of a compressible fluid with large sound speed is near to that of an idealized incompressible fluid. We consider the compressible fluid motion in Lagrangian coordinates and show
that it can be defined by two functions giving the kinetic
and potential energies. The minimal set for the potential
energy is the configuration space of incompressible fluid
motion. If the equation of state of the compressible fluid
is changed so that the sound speed increases, the mini-mum of the potential energy function becomes sharper. The compressible fluid motion approaches a curve in the
minimal set and this curve defines an incompressible fluid motion.