Japan Journal of Industrial and Applied Mathematics

, 9:431

The global weak solutions of compressible Euler equation with spherical symmetry


  • Tetu Makino
    • Department of Liberal ArtsOsaka Sangyo University
  • Kiyoshi Mizohata
    • Department of Information SciencesTokyo Institute of Technology
  • Seiji Ukai
    • Department of Information SciencesTokyo Institute of Technology

DOI: 10.1007/BF03167276

Cite this article as:
Makino, T., Mizohata, K. & Ukai, S. Japan J. Indust. Appl. Math. (1992) 9: 431. doi:10.1007/BF03167276


We shall study the compressible Euler equation which describes the motion of an isentropic gas. Many global existence theorems have been obtained for the one dimensional case. On the other hand, little is known for the casen>-2. No global weak solutions have been known to exist, but only local classical solutions. In this paper, we will present global weak solutions first for the casen>-2. We will do this, however, only for the case of spherical symmetry with γ=1, by using a modified Glimm’s method.

Key words

compressible Euler equationshock waveRiemann invariantGlimm’s difference scheme

Copyright information

© JJIAM Publishing Committee 1992