We consider the $SO(d)$-equivariant Yang-Mills heat flow \begin{ equation*} \partial_t u-\partial_r^2 u-\frac{ (d-3)}{ r}\partial_r u+\frac{ (d-2)}{ r^2}u(1-u)(2-u)=0 \end{ equation*} in dimensions $d>10.$ We construct a family of $\mathcal{ C}^{ \infty}$ solutions which blow up in finite time via concentration of a universal profile \begin{ equation*} u(t,r)\sim Q\left(\frac{ r}{ \lambda(t)}\right), \end{ equation*}where $Q$ is a stationary state of the equation and the blow-up rates are quantized by \begin{ equation*} \lambda(t)\sim c_{ u}(T-t)^{ \frac{ l}{ \gamma}},\,\,\,l\,\,\,\text{ is any positive integer},\,\,\,\gamma=\gamma(d)=\frac{ d-4-\sqrt{ (d-6)^2-12}}{ 2}. \end{ equation*} Moreover, such solutions are in fact $(l-1)$-codimension stable under pertubation of the initial data.
Categories: math.AP