Global well-posedness for the Yang-Mills equation in $4+1$ dimensions. Small energy

Pages 831-893 from Volume 185 (2017), Issue 3 by Joachim Krieger, Daniel Tataru

Abstract

We consider the hyperbolic Yang-Mills equation on the Minkowski space $\mathbb{R}^{4+1}$. Our main result asserts that this problem is globally well-posed for all initial data whose energy is sufficiently small. This solves a longstanding open problem.

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Keywords
, , , ,
Mathematical Subject Classification
Primary: ,
DOI
https://doi.org/10.4007/annals.2017.185.3.3
MR
3664812
Zbl
06731859
Milestones
Received: 7 September 2015
Revised: 22 June 2016
Accepted: 5 July 2016
Published online: 12 April 2017

Authors

Joachim Krieger

École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

Daniel Tataru

The University of California at Berkeley, Berkeley, CA