Long-time existence for Yang-Mills flow

TL;DR

This paper proves that four-dimensional Yang-Mills flow does not develop finite-time singularities, using energy identities and decay estimates, confirming a longstanding conjecture in the field.

Contribution

It provides a rigorous proof ruling out finite-time singularities in 4D Yang-Mills flow, advancing understanding of its long-term behavior.

Findings

Finite-time singularities are ruled out in 4D Yang-Mills flow.

Weighted energy identities are key to the proof.

Sharp decay estimates in neck regions are established.

Abstract

We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck region.