Abstract We study the heat flow for Yang-Mills connections on It is well-known that in dimensions this model admits homothetically shrinking solitons, i.e., self-similar blowup solutions, with an explicit example given by Weinkove. We prove the nonlinear asymptotic stability of the Weinkove solution under small equivariant perturbations and thus extend a result by the second author and Donninger for d = 5 to higher dimensions. At the same time, we provide a general framework for proving stability of self-similar blowup solutions to a large class of semilinear heat equations in arbitrary space dimension including a robust and simple method for solving the underlying spectral problems.

中文翻译：

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等变情况下同位收缩杨-米尔斯孤子的非线性稳定性

摘要 我们研究了Yang-Mills 连接的热流 众所周知，该模型在维度上承认同位收缩孤子，即自相似爆破解，Weinkove 给出了一个明确的例子。我们证明了 Weinkove 解在小等变扰动下的非线性渐近稳定性，从而将第二作者和 Donninger 对 d = 5 的结果扩展到更高维度。同时，我们提供了一个通用框架，用于证明任意空间维度中一大类半线性热方程的自相似爆破解的稳定性，包括用于解决潜在光谱问题的稳健而简单的方法。