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Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

We show that global asymptotically flat singularity-free solutions of the spherically symmetric Vlasov-Einstein system exist for all initial data which are sufficiently small in an appropriate sense. At the same time detailed information is obtained concerning the asymptotic behaviour of these solutions. A key element of the proof which is also of intrinsic interest is a local existence theorem with a continuation criterion which says that a solution cannot cease to exist as long as the maximum momentum in the support of the distribution function remains bounded. These results are contrasted with known theorems on spherically symmetric dust solutions.

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1. Mathematisches Institut der Universität München, Theresienstr. 39, W-8000, München 2, Germany

   G. Rein

2. Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, W-8046, Garching bei München, Germany

   A. D. Rendall

1. G. Rein
2. A. D. Rendall

Communicated by S.-T. Yau

Rein, G., Rendall, A.D. Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data. Commun.Math. Phys. 150, 561–583 (1992). https://doi.org/10.1007/BF02096962

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• Received: 25 March 1992

• Issue Date: December 1992

• DOI: https://doi.org/10.1007/BF02096962

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