2026/07/29 by Johannes Angerer, Sarah Kistner, Birgit Schörkhuber
Mathematics · #math.AP
arxiv created 2026/07/29 · arxiv updated 2026/07/30
We study singularity formation for the heat flow of harmonic maps from \Rd into \mathbbSd in supercritical dimensions d ∈ \3,4,5,6\. It is well known that in each of these dimensions there exist infinitely many self-similar solutions that provide examples of loss of regularity in finite time. In this paper, we extend the results of \citeBieDon18, \citeBieDonSch17 for d=3 to higher space dimensions d ∈ \4,5,6\ and prove the existence of a monotonically increasing self-similar profile f0, which is asymptotically stable under small corotational perturbations. To construct the solution and resolve the spectral problem, we use rigorous computer assistance. As a byproduct of our stability analysis, we also obtain finite-codimension stability of arbitrary self-similar profiles within the corotational class.