PreprintarXiv licencearXiv
Uniqueness of the weak solutions of the Yang-Mills flow in four dimensions
Abstract
We improve a parabolic version of Uhlenbeck's gauge fixing theorem for the Yang-Mills flow. This allows us to prove new existence of weak solutions of the Yang-Mills flow having with better properties than Struwe's weak solution on four manifolds in \cite {St2}. Finally, we apply the new parabolic version of Uhlenbeck's gauge fixing theorem to solve the Struwe problem in \cite {St2} and prove uniqueness of weak solutions to the Yang-Mills flow on compact four-manifolds with initial value A0 ∈ W1, 2(M).
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BibTeX
@misc{chan2026uniqueness,
title = {{Uniqueness of the weak solutions of the Yang-Mills flow in four dimensions}},
author = {Chak Hoi Chan and Min-Chun Hong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38134},
eprint = {2610.38134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38134},
}
RIS
TY - UNPB
TI - Uniqueness of the weak solutions of the Yang-Mills flow in four dimensions
AU - Chak Hoi Chan
AU - Min-Chun Hong
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38134
UR - https://arxiv.org/abs/2610.38134
AB - We improve a parabolic version of Uhlenbeck's gauge fixing theorem for the Yang-Mills flow. This allows us to prove new existence of weak solutions of the Yang-Mills flow having with better properties than Struwe's weak solution on four manifolds in \cite {St2}. Finally, we apply the new parabolic version of Uhlenbeck's gauge fixing theorem to solve the Struwe problem in \cite {St2} and prove uniqueness of weak solutions to the Yang-Mills flow on compact four-manifolds with initial value A_0 ∈ W^1, 2(M).
ER -