Stable blowup for the supercritical Yang-Mills heat flow

Roland Donninger; Birgit Schörkhuber

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arXiv · 1604.07737

Stable blowup for the supercritical Yang-Mills heat flow

Roland Donninger·Birgit Schörkhuber

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Abstract

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 \cite{Wei04}. 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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BibTeX RIS

Roland Donninger, Birgit Schörkhuber. 2016-04-26. Stable blowup for the supercritical Yang-Mills heat flow. https://arxiv.org/abs/1604.07737

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