Non-self similar blowup solutions to the higher dimensional Yang Mills heat flows

In this paper, we consider the Yang-Mills heat flow on R^d×SO(d) with d≥11. Under a certain symmetry preserved by the flow, the Yang-Mills equation can be reduced to the following nonlinear equation: ∂_tu=∂_r²u+[Formula presented]∂_ru−3(d−2)u²−(d−2)r²u³, and (r,t)∈R₊×R₊. We are interested in describing the singularity formation of this parabolic equation. More precisely, we aim to construct non self-similar blowup solutions in higher dimensions d≥11, and prove that the asymptotic behavior of the solution is of the form u(r,t)∼[Formula presented]), as t→T, where Q is the steady state corresponding to the boundary conditions Q(0)=−1,Q^′(0)=0 and the blowup speed λ_ℓ satisfies λ_ℓ(t)=(C(u₀)+o_t→T(1))(T−t)^{[Formula presented]} as t→T,ℓ∈N₊^⁎,α>1. In particular, the case ℓ=1 corresponds to the stable type II blowup regime, whereas for the cases ℓ≥2 corresponds to a finite co-dimensional stable regime. Our approach here is not based on energy estimates but on a careful construction of time dependent eigenvectors and eigenvalues combined with maximum principle and semigroup pointwise estimates.