PreprintCC BY 4.0arXiv
An exact unstable mode of self-similar Yang--Mills solutionsin 5+1 dimensions
Abstract
Self-similar solutions play an important role in the formation of singularities in the Yang--Mills equations. In five space dimensions, these equations admit infinitely many self-similar solutions with an increasing number of unstable modes. It was observed numerically that all excited profiles share the least unstable eigenvalue λ=5. We explain this remarkable spectral property by an elementary construction of the corresponding eigenfunction in terms of the profile.
Related
- Existence of a third self-similar solution of the Yang--Mills equation in high odd dimensions
- Decay estimates for Yang-Mills connections and Yang-Mills-Higgs pairs in higher dimensions
- Uniqueness of the weak solutions of the Yang-Mills flow in four dimensions
- Self-similar solutions to the steady Navier-Stokes equations in arbitrarily high dimensions
- The Exact Overlaps Conjecture for Self-Similar Measures on the Real Line
BibTeX
@misc{bizon2026exact,
title = {{An exact unstable mode of self-similar Yang--Mills solutionsin 5+1 dimensions}},
author = {Piotr Bizoń},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04861},
eprint = {2611.04861},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04861},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An exact unstable mode of self-similar Yang--Mills solutionsin 5+1 dimensions
AU - Piotr Bizoń
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04861
UR - https://arxiv.org/abs/2611.04861
AB - Self-similar solutions play an important role in the formation of singularities in the Yang--Mills equations. In five space dimensions, these equations admit infinitely many self-similar solutions with an increasing number of unstable modes. It was observed numerically that all excited profiles share the least unstable eigenvalue λ=5. We explain this remarkable spectral property by an elementary construction of the corresponding eigenfunction in terms of the profile.
ER -