Interaction of rarefaction waves of the two-dimensional self-similar Euler equations. (English) Zbl 1170.76021

Summary: We construct classical self-similar solutions to the interaction of two arbitrary planar rarefaction waves for the polytropic Euler equations in two space dimensions. The binary interaction represents a major type of interaction in two-dimensional Riemann problems, and includes in particular the classical problem of the expansion of a wedge of gas into vacuum. Based on the hodograph transformation, the method employed here involves the phase space analysis of a second-order equation and the inversion back to (or development onto) the physical space.


76L05 Shock waves and blast waves in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
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