Generic Self-Similar Blowup for Equivariant Wave Maps and Yang–Mills Fields in Higher Dimensions

Abstract

We consider equivariant wave maps from the $(d+1)$--dimensional Minkowski spacetime into the $d$-sphere for $d\geq 4$. We find a new explicit stable self-similar solution and give numerical evidence that it plays the role of a universal attractor for generic blowup. An analogous result is obtained for the $SO(d)$ symmetric Yang-Mills field for $d\geq 6$.