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15 June 2015 Finite energy global well-posedness of the Yang–Mills equations on R 1 + 3 : An approach using the Yang–Mills heat flow
Sung-Jin Oh
Duke Math. J. 164(9): 1669-1732 (15 June 2015). DOI: 10.1215/00127094-3119953

Abstract

In this work, we propose a novel approach to the problem of gauge choice for the Yang–Mills equations on the Minkowski space R 1 + 3 . A crucial ingredient is the associated Yang–Mills heat flow. As this approach avoids the drawbacks of previous approaches, it is expected to be more robust and easily adaptable to other settings. Building on the author’s previous results, we prove, as the first application of our approach, finite energy global well-posedness of the Yang–Mills equations on R 1 + 3 . This is a classical result first proved by Klainerman and Machedon using local Coulomb gauges. As opposed to their method, the present approach avoids the use of Uhlenbeck’s lemma and hence does not involve localization in space-time.

Citation

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Sung-Jin Oh. "Finite energy global well-posedness of the Yang–Mills equations on R 1 + 3 : An approach using the Yang–Mills heat flow." Duke Math. J. 164 (9) 1669 - 1732, 15 June 2015. https://doi.org/10.1215/00127094-3119953

Information

Received: 30 November 2012; Revised: 26 July 2014; Published: 15 June 2015
First available in Project Euclid: 15 June 2015

zbMATH: 1325.35180
MathSciNet: MR3357182
Digital Object Identifier: 10.1215/00127094-3119953

Subjects:
Primary: 35Q99
Secondary: 70S15

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 9 • 15 June 2015
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