Lars Andersson, Nishanth Gudapati, Jeremie Szeftel
Published 2015-01-04Version 1
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.
Global regularity of wave maps II. Small energy in two dimensions
Global regularity for a family of 3D models of the axisymmetric Navier-Stokes equations
Global regularity for the energy-critical NLS on $\mathbb{S}^3$
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