Conjecture on finite-time blowup and instanton profile in dimension four

Consider equation

for the radial Yang–Mills function $w(t,r)$, with $w_{rr}(t,0)$ denoting its second radial derivative at the center. Let $W_S(r)$ be the instanton profile, and let $\lambda(t)$ be a positive scale factor. **Blowup conjecture in $D=4$.** Solutions of equation

with sufficiently large energy should blow up in finite time, in the sense that $w_{rr}(t,0)$ diverges as $t\nearrow T$ for some $T>0$. More precisely, there should exist a positive function $\lambda(t)\searrow0$ as $t\nearrow T$ such that

$$\lim_{t\nearrow T}u(t,\lambda(t)r)=W_S(r).$$

This conjecture formalizes the numerical observation that large-energy solutions form a shrinking, scale-evolving instanton, while small-energy solutions disperse. The supplied text gives numerical evidence but no resolution of the conjecture.