  The behaviour of the solutions to the Riemann problem for the isentropic
Euler equations when the pressure vanishes is analysed. It is shown that any
solution composed of a 1-shock wave and a 2-rarefaction wave tends to a
two-shock wave when the pressure gets smaller than a fixed value determined by
the Riemann data; by contrast, any solution composed of a 1-rarefaction wave
and a 2-shock wave tends to a two-rarefaction wave. The two situations are
illustrated with numerical tests.
