Conformal-type energy estimates on hyperboloids and the wave-Klein-Gordon model of self-gravitating massive fields

Senhao Duan ¹

Yue Ma ²

Weidong Zhang ²

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Département ingénierie Mathématique et informatique, École des Ponts ParisTech, Paris, 77420, France |

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China |

Publication type: Journal Article

Publication date: 2023-04-23

American Institute of Mathematical Sciences (AIMS)

Journal: Communications in Analysis and Mechanics

SJR: —

CiteScore: 0.7

Impact factor: —

ISSN: 28363310

DOI: 10.3934/cam.2023007

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Abstract

<abstract><p>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.</p></abstract>

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Publisher

American Institute of Mathematical Sciences (AIMS)

Journal

Communications in Analysis and Mechanics

SJR

—

CiteScore

0.7

Impact factor

—

ISSN

28363310 (Print)

Conformal-type energy estimates on hyperboloids and the wave-Klein-Gordon model of self-gravitating massive fields

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