Communications in Mathematical Physics

, Volume 271, Issue 3, pp 635–647 | Cite as

On Two-Dimensional Sonic-Subsonic Flow

  • Gui-Qiang Chen
  • Constantine M. Dafermos
  • Marshall Slemrod
  • Dehua Wang


A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-dimensional Euler equations for steady irrotational flows that may contain stagnation points. Only crude estimates are required for establishing compactness. It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points over an obstacle, such as an airfoil, may be realized as limits of sequences of strictly subsonic flows. Furthermore, sonic-subsonic flows may be constructed from approximate solutions. The compactness framework is then extended to self-similar solutions of the Euler equations for unsteady irrotational flows.


Weak Solution Euler Equation Stagnation Point Young Measure National Science Foundation Grant 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Gui-Qiang Chen
    • 1
  • Constantine M. Dafermos
    • 2
  • Marshall Slemrod
    • 3
  • Dehua Wang
    • 4
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA
  3. 3.Department of MathematicsUniversity of WisconsinMadisonUSA
  4. 4.Department of MathematicsUniversity of PittsburghPittsburghUSA

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