Archive for Rational Mechanics and Analysis

, Volume 201, Issue 3, pp 1069–1096 | Cite as

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

  • Mingjie Li
  • Yuxi ZhengEmail author


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.


Rarefaction Wave Riemann Problem Simple Wave Compressible Euler Equation Sonic Point 


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  2. 2.Institute of Applied MathematicsAMSS, Academia SinicaBeijingChina
  3. 3.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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