Interaction of rarefaction waves of the two-dimensional self-similar Euler equations

Jiequan Li, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

113 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)623-657
Number of pages35
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - Jul 1 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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