Note on the Riemann solutions to the Euler equations of gas dynamics in the vanishing pressure limit

The behaviour of the solutions of the Riemann problem for the isentropic Euler equations in vanishing pressure limit is analyzed. It is shown that any solution composed of a 1-shock wave combined with a 2-rarefaction wave tends to a two-shock waves when the pressure coefficient gets smaller than a fixed value determined by the Riemann data. In contrast, any solution composed of a 1-rarefaction wave combined with a 2-shock wave tends to a two-rarefaction waves when the pressure coefficient gets smaller than a fixed value determined by the Riemann data. The two situations are illustrated with a numerical test.