学术报告（王金花 2024.12.20）

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.