Threshold for blowup for equivariant wave maps in higher dimensions

Abstract

We consider equivariant wave maps from ${\mathbb{R}}^{d+1}$ to ${\mathbb{S}}^d$ in supercritical dimensions $3\le d\le 6$. Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable manifold of a self-similar solution with one instability.

11 pages, 3 figures