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Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Science, Capital Normal University, 100037, Beijing, China

    Jiequan Li

  2. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Yuxi Zheng

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  1. Jiequan Li
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  2. Yuxi Zheng
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Correspondence to Jiequan Li.

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Communicated by T.-P. Liu

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Li, J., Zheng, Y. Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations. Arch Rational Mech Anal 193, 623–657 (2009). https://doi.org/10.1007/s00205-008-0140-6

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