Stable blow-up solutions for the SO(d)-equivariant supercritical Yang-Mills heat flow

2021/12/26 by Yezhou Yi, Yi, Yezhou
Mathematics · #35B40 #35K15 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.13325

openalex publication_date 2021/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the SO(d)-equivariant Yang-Mills heat flow ∂_t u-∂_r² u-((d-3))/(r)∂_r u+((d-2))/(r²)u(1-u)(2-u)=0 in dimensions d>10. We construct a family of C^∞ solutions which blow up in finite time via concentration of a universal profile u(t,r)∼ Q((r)/(λ(t))),where Q is a stationary state of the equation and the blow-up rates are quantized by λ(t)∼ c_u(T-t)^\fraclγ, l is any positive integer, γ=γ(d)=(d-4-√((d-6)²-12))/(2). Moreover, such solutions are in fact (l-1)-codimension stable under pertubation of the initial data.

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