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#### The global existence of Yang-Mills fields on curved space-times

##### MPG-Autoren

Ghanem,  Sari
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

##### Externe Ressourcen
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##### Volltexte (frei zugänglich)

1312.5476.pdf
(Preprint), 453KB

##### Ergänzendes Material (frei zugänglich)
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##### Zitation

Ghanem, S. (2016). The global existence of Yang-Mills fields on curved space-times. Journal of Hyperbolic Differential Equations, 13(3), 603-631. doi:10.1142/S0219891616500156.

This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski parametrix combined with suitable Gr\"onwall type inequalities. While the Chru\'sciel-Shatah argument requires a simultaneous control of the $L^{\infty}_{loc}$ and the $H^{2}_{loc}$ norms of the Yang-Mills curvature, we can get away by controlling only the $H^{1}_{loc}$ norm instead, and write a new gauge independent proof on arbitrary, fixed, sufficiently smooth, globally hyperbolic, curved 4-dimensional Lorentzian manifolds. This manuscript is written in an expository way in order to provide notes to Master's level students willing to learn mathematical General Relativity.