@article{Duan2023, 
author = {Senhao Duan and Yue MA and Weidong Zhang},
title = {Conformal-type energy estimates on hyperboloids and the wave-Klein-Gordon model of self-gravitating massive fields},
year = {2023},
journal = {Communications in Analysis and Mechanics},
volume = {15},
number = {2},
pages = {111-131},
keywords = {conformal energy estimate, partial conformal symmetry, Einstein-massive field system, wave-Klein-Gordon system, nonlinear stability},
url = {https://www.sciopen.com/article/10.3934/cam.2023007},
doi = {10.3934/cam.2023007},
abstract = {In this article we revisit the global existence result of the wave-Klein-Gordon model of the system of the self-gravitating massive field. Our new observation is that, by applying the conformal energy estimates on hyperboloids, we obtain mildly increasing energy estimate up to the top order for the Klein-Gordon component, which clarify the question on the hierarchy of the energy bounds of the Klein-Gordon component in our previous work. Furthermore, a uniform-in-time energy estimate is established for the wave component up to the top order, as well as a scattering result. These improvements indicate that the partial conformal symmetry of the Einstein-massive scalar system will play an important role in the global analysis.}
}