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Semi-hyperbolic Patches of Solutions to the Two-dimensional Euler Equations

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Abstract

We construct semi-hyperbolic patches of solutions, in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves, to the two-dimensional Euler equations. This type of solution appears in the transonic flow over an airfoil and Guderley reflection, and is common in the numerical solutions of Riemann problems.

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Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Mingjie Li

  2. Institute of Applied Mathematics, AMSS, Academia Sinica, Beijing, 100190, China

    Mingjie Li

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

    Yuxi Zheng

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

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Communicated by A. Bressan

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Li, M., Zheng, Y. Semi-hyperbolic Patches of Solutions to the Two-dimensional Euler Equations. Arch Rational Mech Anal 201, 1069–1096 (2011). https://doi.org/10.1007/s00205-011-0410-6

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  • DOI: https://doi.org/10.1007/s00205-011-0410-6

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