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September 2019 Stable blowup for the supercritical Yang–Mills heat flow
Roland Donninger, Birgit Schörkhuber
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J. Differential Geom. 113(1): 55-94 (September 2019). DOI: 10.4310/jdg/1567216954


In this paper, we consider the heat flow for Yang–Mills connections on $\mathbb{R}^5 \times SO(5)$. In the $SO(5)$-equivariant setting, the Yang–Mills heat equation reduces to a single semilinear reaction-diffusion equation for which an explicit self-similar blowup solution was found by Weinkove [“Singularity formation in the Yang-Mills flow”, Calc. Var. Partial Differential Equations, 19(2):211–220, 2004]. We prove the nonlinear asymptotic stability of this solution under small perturbations. In particular, we show that there exists an open set of initial conditions in a suitable topology such that the corresponding solutions blow up in finite time and converge to a non-trivial self-similar blowup profile on an unbounded domain. Convergence is obtained in suitable Sobolev norms and in $L^{\infty}$.


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Roland Donninger. Birgit Schörkhuber. "Stable blowup for the supercritical Yang–Mills heat flow." J. Differential Geom. 113 (1) 55 - 94, September 2019.


Received: 17 June 2016; Published: September 2019
First available in Project Euclid: 31 August 2019

zbMATH: 07104703
MathSciNet: MR3998907
Digital Object Identifier: 10.4310/jdg/1567216954

Rights: Copyright © 2019 Lehigh University

Vol.113 • No. 1 • September 2019
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