GRADIENT FLOWS OF HIGHER ORDER YANG–MILLS–HIGGS FUNCTIONALS

Abstract In this paper, we define a family of functionals generalizing the Yang–Mills–Higgs on closed Riemannian manifold. Then prove short-time existence corresponding gradient flow by gauge-fixing technique. The lack maximum principle for higher order operator brings us lot inconvenience during estimates Higgs field. We observe that $L^2$ -bound field is enough energy in four dimensions and show that, provided derivatives appearing strictly greater than one, solutions to do not hit any finite-time singularities. As k -functional with self-interaction, $\dim (M)<2(k+1)$ , every smooth initial data associated admits long-time existence. proof depends local -derivative estimates, blow-up analysis.