Advertisement

Communications in Mathematical Physics

, Volume 150, Issue 3, pp 585–591 | Cite as

The Newtonian limit of the spherically symmetric Vlasov-Einstein system

  • G. Rein
  • A. D. Rendall
Article

Abstract

We prove that spherically symmetric solutions of the Vlasov-Einstein system with a fixed initial value converge to the corresponding solution of the Vlasov-Poisson system if the speed of lightc is taken as a parameter and tends to infinity. The convergence is uniform on compact time intervals with convergence rate 1/c2. Thus the classical Vlasov-Poisson system appears as the Newtonian limit of the general relativistic Vlasov-Einstein system in a spherically symmetric setting.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Convergence Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Asano, K., Ukai, S.: On the Vlasov-Poisson limit of the Vlasov-Maxwell equations. Stud. Math. Appl.18, 369–383 (1986)Google Scholar
  2. 2.
    Batt, J., Rein, G.: Global classical solutions of the periodic Vlasov-Poisson system in three dimensions. C. R. Acad. Sc. Paris.313, 411–416 (1991)Google Scholar
  3. 3.
    Degond, P.: Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity. Math. Meth. Appl. Sci.8, 533–558 (1986)Google Scholar
  4. 4.
    Ehlers, J.: The Newtonian limit of general relativity. In: Ferrarese, G. (ed.) Classical mechanics and relativity: Relationship and consistency. Naples: Bibliopolis 1991Google Scholar
  5. 5.
    Horst, E.: On the asymptotic growth of the solutions of the Vlasov-Poisson system. Preprint 1991Google Scholar
  6. 6.
    Lions, P.-L., Perthame, B.: Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math.105, 415–430 (1991)CrossRefGoogle Scholar
  7. 7.
    Pfaffelmoser, K.: Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J. Diff. Eqns.95, 281–303 (1992)CrossRefGoogle Scholar
  8. 8.
    Rein, G.: Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics. Commun. Math. Phys.135, 41–78 (1990)CrossRefGoogle Scholar
  9. 9.
    Rein, G., Rendall, A.: Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data. Commun. Math. Phys.150, 561–583 (1992)Google Scholar
  10. 10.
    Schaeffer, J.: The classical limit of the relativistic Vlasov-Maxwell system. Commun. Math. Phys.104, 403–421 (1986)CrossRefGoogle Scholar
  11. 11.
    Schaeffer, J.: Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions. Commun. Part. Diff. Eqns.16, 1313–1335 (1991)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • G. Rein
    • 1
  • A. D. Rendall
    • 2
  1. 1.Mathematisches Institut der Universität MünchenMünchen 2Germany
  2. 2.Max-Planck-Institut für AstrophysikGarchingGermany

Personalised recommendations