Generic self-similar blowup for equivariant wave maps and Yang-Mills fields in higher dimensions

TL;DR

This paper discovers a new stable self-similar solution in higher-dimensional equivariant wave maps and Yang-Mills fields, suggesting it acts as a universal attractor for blowup phenomena.

Contribution

It introduces explicit stable self-similar solutions in higher dimensions and provides numerical evidence of their role as universal blowup attractors.

Findings

Existence of a new explicit stable self-similar solution

Numerical evidence of the solution as a universal attractor

Applicable to both 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 $d\geq 6$.