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


DOI: 10.1007/s00205-008-0140-6

Cite this article as:
Li, J. & Zheng, Y. Arch Rational Mech Anal (2009) 193: 623. doi:10.1007/s00205-008-0140-6


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.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

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

Personalised recommendations