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The Riemann problem for the transportation equations in gas dynamics. (English) Zbl 0913.35082
The Riemann problem is considered for the compressible two-dimensional Euler equations under the assumption that pressure is constant. Two types of solutions are discovered. The first involves vacuum and the second is a Dirac delta wave. A vanishing viscosity theorem is proved to show the stability of these solutions and to obtain an entropy condition for the Dirac delta waves.
MSC:
35L65Conservation laws
35L67Shocks and singularities
35L80Hyperbolic equations of degenerate type
65M25Method of characteristics (IVP of PDE, numerical methods)
76N15Gas dynamics, general
76N10Compressible fluids, general