On the blow-up set of the Yang–Mills flow on Kähler surfaces

2006 ◽  
Vol 256 (2) ◽  
pp. 301-310 ◽  
Author(s):  
Georgios D. Daskalopoulos ◽  
Richard A. Wentworth
Keyword(s):  
Blow Up ◽  
Yang Mills ◽  
Kähler Surfaces

Blow‐up of the SU(2,C) Yang–Mills fields

1990 ◽  
Vol 31 (5) ◽  
pp. 1237-1239 ◽  
Author(s):  
Yisong Yang
Keyword(s):  
Blow Up ◽  
Yang Mills

scholarly journals Renormalization and blow up for the critical Yang–Mills problem

2009 ◽  
Vol 221 (5) ◽  
pp. 1445-1521 ◽  
Author(s):  
J. Krieger ◽  
W. Schlag ◽  
D. Tataru
Keyword(s):  
Blow Up ◽  
Yang Mills

scholarly journals GRADIENT FLOWS OF HIGHER ORDER YANG–MILLS–HIGGS FUNCTIONALS

2021 ◽  
pp. 1-31
Author(s):  
PAN ZHANG
Keyword(s):  
Blow Up ◽  
Higgs Field ◽  
Gradient Flow ◽  
Higher Order ◽  
Energy Estimates ◽  
Four Dimensions ◽  
Yang Mills ◽  
Blow Up Analysis ◽  
Long Time Existence ◽  
Time Existence

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

scholarly journals The global non-blow-up of the Yang–Mills curvature on curved space-times

2016 ◽  
Vol 13 (03) ◽  
pp. 603-631 ◽  
Author(s):  
Sari Ghanem
Keyword(s):  
Blow Up ◽  
Lorentzian Manifolds ◽  
Curved Space ◽  
Yang Mills ◽  
Globally Hyperbolic ◽  
Derivatives Of

We give a proof of the non-blow-up of the Yang–Mills curvature on arbitrary curved space-times using the Klainerman–Rodnianski parametrix combined with suitable Grönwall type inequalities. While the Chruściel–Shatah argument requires a control on two derivatives of the Yang–Mills curvature, we can get away by controlling only one derivative instead, and we propose a new gauge-independent proof on sufficiently smooth, globally hyperbolic, curved 4-dimensional Lorentzian manifolds.

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