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A limiting viscosity approach for the Riemann problem in isentropic gas dynamics. (English) Zbl 0675.76073

We consider the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates. We construct solutions of this problem as limits of solutions of a “viscosity” regularized problem that is rigged so as to preserve the invariance of the original problem under dilatations of the independent variables. The solutions thus constructed may contain vacuum regions. Using the same approach we also construct solutions of the Riemann problem in case the data contain a vacuum state.
Reviewer: M.Slemrod

MSC:

76N15 Gas dynamics (general theory)
35Q30 Navier-Stokes equations
35L67 Shocks and singularities for hyperbolic equations
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