Self-similar blowup from arbitrary data for supercritical wave maps with additive noise

Abstract

We consider stochastically perturbed wave maps from ${\mathbb{R}}^{1+d}$ into ${\mathbb{S}}^d$, in all energy-supercritical dimensions $d\ge 3$. We show that corotational non-degenerate Gaussian additive noise leads to self-similar blowup with positive probability for any corotational initial data. The same result without noise is conjectured, but unknown, for large data.

35 Pages