Bizoń et al.'s large-data blow-up conjecture for equivariant wave maps

Let $(\vartheta,\partial_t\vartheta)|_{t=0}$ be initial data satisfying the initial-data condition in

, and let $\vartheta(t,r)$ solve the equivariant wave-map equation

. For sufficiently large energy, the solution blows up in finite time, meaning that

$$\partial_r\vartheta(t,0)\to\infty$$

as $t\nearrow T$ for some $T>0$.

Bizoń et al.'s large-data blow-up conjecture. For initial data

$$with sufficiently large energy, the corresponding solutions of$$

blow up in finite time in this sense.

This is one of three conjectures formulated from numerical observations of singularity formation for the equivariant $2+1$-dimensional wave map into the $2$-sphere. The source gives no resolution status for this claim.