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

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.

final version

References in corpus (1)

• Regularization of spherical and axisymmetric evolution codes in numerical relativity

Cited by in corpus (1)

• High-frequency backreaction for the Einstein equations under polarized $\mathbb{U}(1)$ symmetry