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The interaction of rarefaction waves of the two-dimensional Euler equations. (English) Zbl 1203.35167

This paper deals with the interaction of rarefaction waves of the two-dimensional Euler equations using characteristics analysis. It contains basic material on the system in self-similar variables, and provides equations for the variables of inclination angles, velocity, and the speed of sound. It describes an expansion problem of a wedge into vacuum, which is the interaction of two planar rarefaction waves. The estimates of data on the boundaries of the expansion problem, and on the derivatives of velocity are given.

MSC:

35L65 Hyperbolic conservation laws
35J70 Degenerate elliptic equations
35R35 Free boundary problems for PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35Q31 Euler equations
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