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VOL. 85 | 2020 Global regularity for Einstein-Klein Gordon system with $U(1) \times \mathbb{R}$ isometry group
Haoyang Chen, Yi Zhou

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

Abstract

This is an announcement of [3] and [4] which study the global regularity of the 3+1 dimensional Einstein-Klein Gordon system with a $U(1) \times \mathbb{R}$ isometry group. We reduce the Cauchy problem of the Einstein-Klein Gordon system to a 2+1 dimensional system. Next, the energy of this system cannot concentrate near the first possible singularity, and hence is small. Then, we show that the global regularity holds for the reduced 2+1 system with initial data of small energy.

Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510533

Subjects:
Primary: 35L70, 35Q76

Rights: Copyright © 2020 Mathematical Society of Japan

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