On Asymptotic Behavior of Elliptic SO(d)-Equivariant Yang–Mills Fields

Abstract

We study the solutions of elliptic Yang–Mills equation $-\partial _r^2 u-\frac{(d-3)}{r} \partial _r u+\frac{(d-2)}{r^2}u(1-u)(2-u)=0,$ and we give a description of their asymptotic behaviors in dimensions $d\ge 10$. These solutions serve as the ground state solutions for super-critical Yang–Mills heat flow equation; thus, this result provides the background for potential blow-up research.

Keywords

Yang-Mills fields / Asymptotic behavior / SO(d)-equivariant

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Funding

NSFC(No. 11771415)