# Singularities in Yang Mills Flow

In "The Yang Mills flow in four dimensions", M. Struwe proves that this flow converges, up to bubbling phenomena. And he has conjectured that this explosion in finite time should happen as proven for the harmonic heat flow by Chang, Ding and Ye. Looking on MathSciNet, I have found no proof or disproof of this fact. Is this question still open?

On the other hand, Donaldson proves that if the underlying bundle is stable there is a global existence. Has this hypothesis been weakened?

• In terms of global existence, the results I am aware of are all under symmetry assumptions. There's originally the work of Schlatter, Struwe, and Tahvildar-Zadeh (1998) which proved global existence for $SU(2)$ over $\mathbb{R}^4$ under an equivariance assumption, and this has been generalised a bit by Hong and Tian (2004). – Willie Wong Jun 13 '14 at 9:04