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Global weak solutions of the compressible Euler equation with spherical symmetry (II)

  • Tetu Makino
  • Kiyoshi Mizohata
  • Seiji Ukai
Article

Abstract

We study the spherically symmetric motion of isothermal gas surrounding a ball. Recently we constructed global weak solutions for the initial boundary value problem in [2], but the class of the initial data considered there was not wide enough to include the stationary solutions for which the density is constant on the whole space. In this paper we will extend our preceding result to a wider class of the initial data so that it includes such stationary solutions. To do this, we will present a modification of Glimm’s method in which the mesh lengths for approximate solutions are not uniform.

Key words

compressible Euler equation shock wave Riemann invariant Glimm’s difference scheme 

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References

  1. [1]
    J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math,18 (1965), 697–715.MATHCrossRefMathSciNetGoogle Scholar
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    T. Makino, K. Mizohata and S. Ukai, The global weak solutions of the compressible Euler equation with spherical symmetry. Japan J. Indust. Appl. Math.,9 (1992), 431–449.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    K. Mizohata, Global weak solutions for the equation of isothermal gas around a star. Preprint.Google Scholar
  4. [4]
    K. Mizohata, Equivalence of Eulerian and Lagrangian weak solutions of the compressible Euler equation with spherical symmetry. Preprint.Google Scholar
  5. [5]
    T. Nishida, Global solutions for an initial boundary value problem of a quasilinear hyperbolic system. Proc. Japan Acad.,44 (1968), 642–646.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© JJIAM Publishing Committee 1994

Authors and Affiliations

  • Tetu Makino
    • 1
  • Kiyoshi Mizohata
    • 2
  • Seiji Ukai
    • 2
  1. 1.Department of Liberal ArtsOsaka Sangyo UniversityOsakaJapan
  2. 2.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan

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