Global-in-space stability of singularity formation for Yang-Mills fields in higher dimensions

We continue our work [16] 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≥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.