The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit (Q1088550)

The author considers the Euler equations for nonisentropic compressible inviscid fluids in a bounded domain. The description of the fluid is completed by the equation of state \(\rho =f(P/\lambda^ 2,S)\) where \(\rho\) is the density, P the pressure, S the entropy and the parameter \(\lambda\) is essentially the inverse of the Mach number. First the author proves the local (in time) existence of a classical solution for any fixed \(\lambda\). Afterwards he shows that the solutions converge, as \(\lambda \to +\infty\), to the corresponding solution of the equations for incompressible inviscid fluids with variable density.