Stable blowup for the supercritical hyperbolic Yang-Mills equations

TL;DR

This paper demonstrates the stability of self-similar blowup solutions in supercritical hyperbolic Yang-Mills equations for odd dimensions five and above, supporting their role as universal attractors for large data.

Contribution

It proves the stability of a known blowup mechanism in supercritical Yang-Mills equations for odd dimensions, advancing understanding of singularity formation.

Findings

Self-similar blowup solutions are stable in odd dimensions ≥ 5.

Supports the conjecture that these solutions are universal attractors.

Provides partial proof of the blowup mechanism's stability.

Abstract

We consider the Yang-Mills equations in $(1+d)$-dimensional Minkowski spacetime. It is known that in the supercritical case, i.e., for $d \geq 5$, these equations admit closed form equivariant self-similar blowup solutions \cite{BieBiz15}. These solutions are furthermore conjectured to be the universal attractors for generic large equivariant data evolutions. In this paper we partially prove this conjecture. Namely, we show that for all odd $d \geq 5$ the blowup mechanism exhibited by these solutions is stable.