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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, Bei**g, 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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  • DOI: https://doi.org/10.1007/s00205-008-0140-6

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