题目：Extension principle for the spherically symmetric Einstein Yang--Mills equations

报告人：王金花 副教授（厦门大学）

时间：2025/01/10  周五上午10:00-11:00 腾讯会议：548-473-228

邀请人：张华丽

摘要：We establish an extension principle for the spherically symmetric Einstein Yang--Mills system (SSEYM) with $H^1$ data. Based on this result, we further prove an extension theorem for developments of weighted $H^1$ data. In particular, the weighted $H^1$ space allows H\"{o}lder continuous data. Therefore, our result is consistent with the conjecture that the well-posedness including the axis holds for H\"{o}lder continuous data (with sufficiently many angular derivatives) in vacuum.

Different from a massless scalar field, the purely magnetic Yang--Mills field in spherical symmetry satisfies a wave type equation with a singular potential. The proof of Christodoulou which were based on an $L^\infty-L^\infty$ estimate fails for the Yang--Mills case. Instead, we employ the $L^2$ method, which works for the (massless or massive) scalar matter field as well. This is joint work with Junbin Li.

报告人简介：

王金花，厦门大学副教授。2013年浙江大学博士毕业，2013-2016德国马普所-爱因斯坦研究所洪堡博士后。研究方向为数学广义相对论，双曲偏微分方程，几何分析。研究兴趣包括爱因斯坦方程（耦合Klein—Gordon，Yang—Mills等物质场），非线性波方程，Lorentz极大子流形（膜方程）的长时间动力学行为, 衰减速度，奇性行为。 主要工作集中于非线性波方程大初值整体解问题，宇宙模型的整体非线性稳定性。相关工作发表于J. Eur. Math. Soc.，Class. Quantum Grav.，Calc. Var. PDE，Ann. Henri Poincaré等杂志。