Higher order Yang-Mills flow

TL;DR

This paper introduces a family of generalized Yang-Mills functionals, analyzes their gradient flows, and establishes long-term existence, convergence, and bubbling criteria across different dimensions, providing alternative proofs for known results.

Contribution

It defines new generalized functionals and studies their gradient flows, offering novel proofs and criteria for convergence and bubbling in Yang-Mills theory.

Findings

Proves long-time existence and convergence of flows in subcritical dimensions.

Establishes bubbling criteria in critical dimensions.

Provides alternative proofs for known Yang-Mills flow results.

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 the critical dimensions. Consequently, we have an alternate proof of the convergence of Yang-Mills flow in dimensions 2 and 3 given by Rade and the bubbling criterion in dimension 4 of Struwe in the case where the initial flow data is smooth.