The Incompressible Limit of the Non-Isentropic Euler Equations

We study the Euler equations for slightly compressible fluids, that is, after rescaling, the limits of the Euler equations of fluid dynamics as the Mach number tends to zero. In this paper, we consider the general non-isentropic equations and general data. We first prove the existence of classical solutions for a time independent of the small parameter. Then, on the whole space ℝ ^d , we prove that the solution converges to the solution of the incompressible Euler equations. Accepted December 1, 2000?Published online April 23, 2001