Annales Henri Poincaré

, Volume 14, Issue 6, pp 1445–1523 | Cite as

Quasilinear Hyperbolic Fuchsian Systems and AVTD Behavior in T2-Symmetric Vacuum Spacetimes

  • Ellery Ames
  • Florian Beyer
  • James Isenberg
  • Philippe G. LeFloch
Article

Abstract

We set up the singular initial value problem for quasilinear hyperbolic Fuchsian systems of first order and establish an existence and uniqueness theory for this problem with smooth data and smooth coefficients (and with even lower regularity). We apply this theory in order to show the existence of smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein equations, which exhibit asymptotically velocity term dominated behavior in the neighborhood of their singularities and are polarized or half-polarized.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Ellery Ames
    • 1
  • Florian Beyer
    • 2
  • James Isenberg
    • 3
  • Philippe G. LeFloch
    • 4
  1. 1.Department of PhysicsUniversity of OregonEugeneUSA
  2. 2.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  3. 3.Department of MathematicsUniversity of OregonEugeneUSA
  4. 4.Laboratoire Jacques-Louis Lions & Centre National de la Recherche ScientifiqueUniversité Pierre et Marie Curie (Paris 6)ParisFrance

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