Higher order Yang–Mills flow

Abstract

We define a family of functionals generalizing the Yang–Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for critical dimensions. Consequently, we generalize the results of the convergence of Yang–Mills flow in dimensions 2 and 3 given by Rade (J Reine Angew Math 431:123–163, 1992) and the bubbling criterion in dimension 4 of Struwe (Calc Var 2:123–150, 1994) in the case where the initial flow data is smooth.