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Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System

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Andersson,  Lars
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1501.00616.pdf
(Preprint), 691KB

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Citation

Andersson, L., Gudapati, N., & Szeftel, J. (2017). Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System. Annals of PDE, 3: 13. doi:10.1007/s40818-017-0030-z.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-0042-7
Abstract
In this paper we consider the equivariant 2+1 dimensional Einstein-wave map system and show that if the target satisfies the so called Grillakis condition, then global existence holds. In view of the fact that the 3+1 vacuum Einstein equations with a spacelike translational Killing field reduce to a 2+1 dimensional Einstein-wave map system with target the hyperbolic plane, which in particular satisfies the Grillakis condition, this work proves global existence for the equivariant class of such spacetimes.