Stable blowup for the supercritical hyperbolic Yang-Mills equations

We consider the Yang-Mills equations in (1 + d)-dimensional Minkowski spacetime. It is known that in the supercritical case, i.e., for d >= 5, these equations admit closed form equivariant self-similar blowup solutions [2]. 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 >= 5 the blowup mechanism exhibited by these solutions is stable.(C) 2022 The Author(s). Published by Elsevier Inc.

Automated summary

This paper considers the Yang-Mills equations in (1 + d)-dimensional Minkowski spacetime. It is known that in the supercritical case, i.e., for d >= 5, these equations admit closed form equivariant self-similar blowup solutions. These solutions are conjectured to be the universal attractors for generic large equivariant data evolutions. In this paper, the authors partially prove this conjecture by showing stability of the blowup mechanism exhibited by these solutions for all odd d >= 5.