数学研究所
学术报告
广义相对论研讨班
Speaker: Sari Ghanem (BIMSA)
Inviter: 马思远 副研究员
Language: English
Title: Dispersive estimates for the Einstein-Yang-Mills fields in the Lorenz gauge with small initial data
Time&Venue: 2025年3月14日（星期五） 14:00-15:00 & Zoom会议: 645 4541 4156 Passcode: 035726
Abstract:I will present the Einstein-Yang-Mills system in both the Lorenz gauge and in wave coordinates, where the Yang-Mills fields are valued in any arbitrary Lie algebra, associated to any compact Lie group. This gives a system of hyperbolic partial differential equations that does not satisfy the null condition and that has new complications that are not present for the Einstein vacuum equations nor for the Einstein-Maxwell system. We then prove exterior dispersive estimates for initial data close to the Minkowski data, for the evolution problem governed by the fully coupled Einstein-Yang-Mills system in the Lorenz gauge, valued in any arbitrary Lie algebra, without any assumption of spherical symmetry. This provides a first detailed proof of the exterior stability of the Minkowski space-time governed by the fully non-linear Einstein-Yang-Mills equations in both the Lorenz and harmonic gauges.
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