Bubbling for Yang–Mills connections

Let $A(t)$ be a smooth finite-energy solution to the Yang–Mills equation on $\mathbb R^{1+4}$, with maximal forward time of existence $T_{+}$. For a sequence of times $t_n\to T_{+}$, scales $\lambda_n=o(T_{+}-t_n)$, and translations $x_n\in\mathbb R^4$, define

$$A_{(n)}(t,x):=\lambda_n A(t_n+\lambda_n t,x_n+\lambda_n x).$$

Bubbling for Yang–Mills. Either $T_{+}=\infty$, or there are such sequences for which $A_{(n)}$ converges, through its curvature, to a Lorentz transform of a nontrivial finite-energy elliptic Yang–Mills connection $B$:

$$F[A_{(n)}]\to F[B]\quad\text{as }n\to\infty\text{ in }L^2_{\mathrm{loc}}((-1,1)\times\mathbb R^4).$$

This is the expected Yang–Mills analogue of bubbling at the finite-time singularity threshold for wave maps. The parser supplies no evidence that the conjecture has been resolved; its status is therefore open.