Global regularity for Einstein-Klein-Gordon system with $U(1) \times \mathbb{R}$ isometry group, II
Analysis of PDEs
2019-05-23 v1
Abstract
This paper is devoted to the study of the global existence of smooth solutions for the 3+1 dimensional Einstein-Klein-Gordon systems with a isometry group for a class of regular Cauchy data. In our first paper \cite{chen}, we reduce the Einstein equations to a 2+1 dimensional Einstein-wave-Klein-Gordon system. And we show that the first possible singularity can only occur at the axis. In this paper, we give a proof for the global regularity for the 2+1 dimensional system. Firstly, we show the non-concentration of the energy near the first possible singularity. Then, we prove that the global regularity holds for initial data with small energy.
Cite
@article{arxiv.1905.08968,
title = {Global regularity for Einstein-Klein-Gordon system with $U(1) \times \mathbb{R}$ isometry group, II},
author = {Haoyang Chen and Yi Zhou},
journal= {arXiv preprint arXiv:1905.08968},
year = {2019}
}