Communications in Mathematical Physics

, Volume 180, Issue 1, pp 153–193

Global solutions to the compressible Euler equations with geometrical structure

  • Gui-Qiang Chen
  • James Glimm

DOI: 10.1007/BF02101185

Cite this article as:
Chen, GQ. & Glimm, J. Commun.Math. Phys. (1996) 180: 153. doi:10.1007/BF02101185


We prove the existence of global solutions to the Euler equations of compressible isentropic gas dynamics with geometrical structure, including transonic nozzle flow and spherically symmetric flow. Due to the presence of the geometrical source terms, the existence results themselves are new, especially as they pertain to radial flow in an unbounded region,\(|\vec x| \geqq 1,\), and to transonic nozzle flow. Arbitrary data withL bounds are allowed in these results. A shock capturing numerical scheme is introduced to compute such flows and to construct approximate solutions. The convergence and consistency of the approximate solutions generated from this scheme to the global solutions are proved with the aid of a compensated compactness framework.

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Gui-Qiang Chen
    • 1
  • James Glimm
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Department of Applied Mathematics and SatisticsState University of New YorkStony BrookUSA