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On the Evolution Problem for the Einstein-Vlasov System

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Abstract

In this work, we solve the evolution problem associated with the Einstein-Vlasov system, with initial data specified on two transversally intersecting null hypersurfaces. The main existence and uniqueness result of the paper is obtained by a contracting mapping principle, combined with Sobolev inequalities and Moser estimates as well as energy inequalities for first order and second order linear hyperbolic systems. The whole investigation is conducted in appropriate weighted Sobolev spaces.

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Acknowledgments

This work was supported by the Abdus Salam International Centre for Theoretical Physics (ICTP, Trieste-Italy) through the Mathematics Research Fellowships and the Regular Associateship programmes. The author thanks the referees for their advice that helped improve the quality of this paper.

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  1. Calvin Tadmon

    Present address: International Centre for Theoretical Physics, Strada Costiera 11, I-34151, Trieste, Italy

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  1. Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon

    Calvin Tadmon

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Tadmon, C. On the Evolution Problem for the Einstein-Vlasov System. Acta Math Vietnam 42, 163–186 (2017). https://doi.org/10.1007/s40306-016-0189-5

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