Duke Mathematical Journal

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

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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.

Article information

Source
Duke Math. J., Volume 164, Number 9 (2015), 1669-1732.

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1434377459

Digital Object Identifier
doi:10.1215/00127094-3119953

Mathematical Reviews number (MathSciNet)
MR3357182

Zentralblatt MATH identifier
1325.35180

Subjects
Primary: 35Q99: None of the above, but in this section
Secondary: 70S15: Yang-Mills and other gauge theories

Keywords
Yang–Mills equations Yang–Mills heat flow gauge choice finite energy global well-posedness

Citation

Oh, Sung-Jin. Finite energy global well-posedness of the Yang–Mills equations on $\mathbb{R}^{1+3}$ : An approach using the Yang–Mills heat flow. Duke Math. J. 164 (2015), no. 9, 1669--1732. doi:10.1215/00127094-3119953. https://projecteuclid.org/euclid.dmj/1434377459


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