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We study the Riemann problem for the system of conservation laws of one dimensional isentropic gas dynamics in Eulerian coordinates. We construct solutions of the Riemann problem by the method of self-similar zero-viscosity limits, where the self-similar viscosity only appears in the equation for the conservation of momentum. No size restrictions on the data are imposed. The structure of the obtained solutions is also analyzed.

A self-similar viscosity approach for the Riemann problem in isentropic gas dynamics and the structure of the solutions