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,

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$-\partial _r^2 u-\frac{(d-3)}{r} \partial _r u+\frac{(d-2)}{r^2}u(1-u)(2-u)=0,$$\end{document}

and we give a description of their asymptotic behaviors in dimensions

d\ge 10

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d\ge 10$$\end{document}

. 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 / 34B15 / 34E05

References

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Funding

NSFC(No. 11771415)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature