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Existence, uniqueness, and local stability for the Einstein-Maxwell-Boltzman system

An existence and uniqueness theorem of the solution of the Cauchy problem for the coupled Einstein-Maxwell-Boltzman system is proven, in an appropriate Sobolev space for the potentials, and weighted Sobolev space for the distribution function. The proof relies on a priori estimates for the collision operator previously established by D.B., and for the solution of the Einstein-Maxwell-Liouville system by Y.C.B. It is also proved here that the solution depends continuously on the data.

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1. Choquet-Bruhat, Y.: Problème de Cauchy pour le système intégro-différentiel d'Einstein-Liouville. Ann. Inst. Fournier, XXI, 3, 1971, p.181–201 and Einstein-Maxwell-Liouville system, volume in the honour of Petrov

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1. Daniel Bancel

   Present address: Département de Mathématiques, Université Paul Sabatier, Toulouse, France

1. Département de Mécanique, Université Paris 6, Paris, France

   Daniel Bancel & Yvonne Choquet-Bruhat

1. Daniel Bancel
2. Yvonne Choquet-Bruhat

Bancel, D., Choquet-Bruhat, Y. Existence, uniqueness, and local stability for the Einstein-Maxwell-Boltzman system. Commun.Math. Phys. 33, 83–96 (1973). https://doi.org/10.1007/BF01645621

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• Received: 20 February 1973

• Issue Date: June 1973

• DOI: https://doi.org/10.1007/BF01645621

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