Motion of a slightly compressible fluid.

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 minimum 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.