Archive for Rational Mechanics and Analysis

, Volume 193, Issue 3, pp 623–657 | Cite as

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

  • Jiequan LiEmail author
  • Yuxi Zheng


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.


Rarefaction Wave Riemann Problem Simple Wave Euler System Riemann Invariant 


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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of Mathematical ScienceCapital Normal UniversityBeijingChina
  2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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