Conjecture on finite-time blowup and universal self-similar profile in dimension five

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 $W_0(r)$ be the stable self-similar solution describing the observed shrinking kink. **Blowup conjecture in $D=5$.** Solutions of equation

corresponding to sufficiently large initial data should blow up in finite time, in the sense that $w_{rr}(t,0)$ diverges as $t\nearrow T$ for some $T>0$, and their universal asymptotic profile should satisfy

$$\lim_{t\nearrow T}w(t,(T-t)r)=W_0(r).$$

This conjecture formalizes the numerical observation that sufficiently strong initial data develop a finite-time singularity whose inner region approaches the stable self-similar profile, whereas small data disperse. The supplied text gives numerical evidence but no resolution of the conjecture.