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Acta Mathematica Vietnamica

, Volume 42, Issue 1, pp 163–186 | Cite as

On the Evolution Problem for the Einstein-Vlasov System

  • Calvin TadmonEmail author
Article
  • 85 Downloads

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.

Keywords

Einstein-Vlasov system Gravitational field Distribution function Evolution problem Sobolev inequalities Moser estimates 

Mathematics Subject Classification (2010)

82D05 83C05 35L03 35L52 

Notes

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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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of DschangDschangCameroon
  2. 2.International Centre for Theoretical PhysicsTriesteItaly

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