Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations
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- Li, J. & Zheng, Y. Arch Rational Mech Anal (2009) 193: 623. doi:10.1007/s00205-008-0140-6
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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 the 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.