Global Regularity for Einstein-Klein-Gordon System with U(1) × R Isometry Group, I

Citation:

Haoyang CHEN,Yi ZHOU.Global Regularity for Einstein-Klein-Gordon System with U(1) × R Isometry Group, I[J].Chinese Annals of Mathematics B,2020,41(6):939~966
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Authors:

Haoyang CHEN; Yi ZHOU

Foundation:

This work was supported by the Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), the Ministry of Education of China, Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, the National Natural Science Foundation of China (Nos. 11421061, 11726611, 11726612), 973 Program (No. 2013CB834100) and 111 Project.
Abstract: This is the first of the two papers devoted to the study of global regularity of the 3 + 1 dimensional Einstein-Klein-Gordon system with a U(1) × R isometry group. In this first part, the authors reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2 + 1 dimensional system. Then, the authors will give energy estimates and construct the null coordinate system, under which the authors finally show that the first possible singularity can only occur at the axis.

Keywords:

Einstein-Klein Gordon system, Cauchy problem, Energy estimates, Null coordinate, First singularity

Classification:

35Q76 35L70
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