高维Yang-Mills场奇点形成的空间全局稳定性
Global-in-space stability of singularity formation for Yang-Mills fields in higher dimensions
AI总结：
本文研究(1+d)维Minkowski空间中Yang-Mills方程在d≥5能量超临界情形下，显式等变自相似爆破解在小等变扰动下的非线性空间全局渐近稳定性，补充了奇数维并首次给出了偶数维的稳定性结果。
摘要：
我们继续文献[Glo22a]中关于径向情形下半线性波动方程的自相似爆破剖面在空间全局稳定性的分析工作。本文研究(1+d)维Minkowski空间中的Yang-Mills方程。对于d≥5的能量超临界情形，我们考虑一个显式已知的等变自相似爆破解，并证明其在小等变扰动下的非线性空间全局渐近稳定性。初始数据的大小用某种意义上缩放以上的最优Sobolev范数来度量。此结果补充了奇数维现有的稳定性结果，而对偶数维而言则是全新的。
英文摘要：
We continue our work \cite{Glo22a} on the analysis of spatially global stability of self-similar blowup profiles for semilinear wave equations in the radial case. In this paper we study the Yang-Mills equations in $(1+d)$-dimensional Minkowski space. For $d \geq 5$, which is the energy supercritical case, we consider an explicitly known equivariant self-similar blowup solution and establish its nonlinear global-in-space asymptotic stability under small equivariant perturbations. The size of the initial data is measured in terms of, in a certain sense, optimal Sobolev norm above scaling. This result complements the existing stability results in odd dimensions, while for even dimensions it is new.
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