Compressible and incompressible fluids

The considered equations of compressible ideal fluid flow in appropriate nondimensional form are a hyperbolic system in four variables, related to density and fluid velocity. The Euler equations of incompressible fluid flow are a distinctly different system of four equations in four unknowns. Qualitative and quantitative properties of a specific limiting process are developed. The new results include more general uniform stability estimates for solutions of the equations of compressible ideal fluid flow. Attention is given to linearized acoustics, asymptotic expansions and long time existence for the compressible equations.