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Acta Mathematica Vietnamica

, Volume 44, Issue 2, pp 501–517 | Cite as

The Einstein-Vlasov-Scalar Field System with Gowdy or T2 Symmetry in Contracting Direction

  • Alex Lassiye Tchuani
  • David TegankongEmail author
  • Norbert Noutchegueme
Article
  • 22 Downloads

Abstract

We prove in the case of cosmological models for the Einstein-Vlasov-scalar field system with Gowdy symmetry, that the solutions exist globally in the past. The sources of the equations are generated by a distribution function and a scalar field, subject to the Vlasov and the wave equations respectively. The result is generalized for the case of T2 symmetry. Using previous results, we deduce geodesic completeness.

Keywords

Einstein Vlasov Scalar field Gowdy symmetry T2 symmetry Hyperbolic differential equations Global existence Geodesic completeness 

Mathematics Subject Classification (2010)

83C20 83C22 34B05 

Notes

Acknowledgements

Comments of the anonymous referee are gratefully acknowledged by the authors.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Alex Lassiye Tchuani
    • 1
  • David Tegankong
    • 2
    Email author
  • Norbert Noutchegueme
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceUniversity of Yaounde 1YaoundeCameroon
  2. 2.Department of Mathematics, ENSUniversity of Yaounde 1YaoundeCameroon

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