Slemrod, Marshall; Tzavaras, Athanasios E. A limiting viscosity approach for the Riemann problem in isentropic gas dynamics. (English) Zbl 0675.76073 Indiana Univ. Math. J. 38, No. 4, 1047-1074 (1989). 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 Cited in 2 ReviewsCited in 22 Documents MSC: 76N15 Gas dynamics (general theory) 35Q30 Navier-Stokes equations 35L67 Shocks and singularities for hyperbolic equations Keywords:Riemann problem; isentropic gas dynamics; Eulerian coordinates; “viscosity” regularized problem; dilatations × Cite Format Result Cite Review PDF Full Text: DOI