Classification for the $2$-equivariant harmonic map heat flow and the radial energy-critical nonlinear heat equation in dimension $6$

We consider the global dynamics of finite-energy solutions to the $2$-equivariant harmonic map heat flow from $\bbR^2$ to $\bbS^2$ and $\dot H^1$-bounded radial solutions to the energy-critical nonlinear heat equation in dimension $6$. Building upon soliton resolution, we obtain a classification of