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This is the second paper in a series studying the nonlinear stability ofrarefaction waves in multi-dimensional gas dynamics. We construct initial datanear singularities in the rarefaction wave region and, combined with the apriori energy estimates from the first paper, demonstrate that any smoothperturbation of constant states on one side of the diaphragm in a shock tubecan be connected to a centered rarefaction wave. We apply this analysis tostudy multi-dimensional perturbations of the classical Riemann problem forisentropic Euler equations. We show that the Riemann problem is structurallystable in the regime of two families of rarefaction waves.

On the stability of multi-dimensional rarefaction waves II: existence of solutions and applications to Riemann problem