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

Uihyeon Jeong, Taegyu Kim

We consider the global dynamics of finite-energy solutions to the $2$-equivariant harmonic map heat flow from ${\mathbb{R}}^2$ to $\bbS^2$ and ${\dot{H}}^1$-bounded radial solutions to the en…