Saratchandran, H.Zhang, J.Zhang, P.2023-01-102023-01-102022Bulletin of the Australian Mathematical Society, 2022; 107(2):320-3290004-97271755-1633https://hdl.handle.net/2440/137205Published online first 29 November 2023Let (M, g) be a closed Riemannian 4-manifold and let E be a vector bundle over M with structure group G, where G is a compact Lie group. We consider a new higher order Yang–Mills–Higgs functional, in which the Higgs field is a section of Ω0(adE). We show that, under suitable conditions, solutions to the gradient flow do not hit any finite time singularities. In the case that E is a line bundle, we are able to use a different blow-up procedure and obtain an improvement of the long-time result of Zhang [‘Gradient flows of higher order Yang–Mills–Higgs functionals’, J. Aust. Math. Soc. 113 (2022), 257–287]. The proof relies on properties of the Green function, which is very different from the previous techniques.en© 2022 Cambridge University Presshigher order Yang–Mills–Higgs flow; line bundle; long-time existenceJournal article10.1017/S00049727220012652023-01-10598534