×

A Yang-Mills-Higgs gradient flow on \(\mathbb{R}^3\) blowing up at infinity. (English) Zbl 0920.58020

From the text: “We prove long time existence of the Yang-Mills-Higgs gradient flow on Euclidean 3-space \(\mathbb{R}^3\), with a geometric characterization at the singular points. Since a solution of the Yang-Mills-Higgs gradient flow constructed in this paper has geometrically reasonable properties at the ideal boundary of \(\mathbb{R}^3\), we are motivated to propose our definition of a global solution for the gradient flow”.

MSC:

58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
81T13 Yang-Mills and other gauge theories in quantum field theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Dostoglou : On the asymptotics of finite energy solutions of the Yang-Mills-Higgs equations. J. Math. Phys., 31, 2490-2496 (1990). · Zbl 0726.58014 · doi:10.1063/1.528992
[2] D. Groisser : Integrality of the monopole number in SU (2) Yang-Mills-Higgs gauge theory on R. Commun. Math. Phys., 93, 367-378 (1984). · Zbl 0564.58039 · doi:10.1007/BF01258535
[3] A. Hassel: The Yang-Mills-Higgs heat flow on R3. J. Funct. Analy., III, 431-448 (1993). · Zbl 0778.35048 · doi:10.1006/jfan.1993.1020
[4] N. J. Hitchin: Monopoles and geodesies. Commun. Math. Phys., 83, 579-602 (1982). · Zbl 0502.58017 · doi:10.1007/BF01208717
[5] A. Jaffe and C. H. Taubes: Vortices and Mono-poles. Birkhauser, Boston (1980). · Zbl 0457.53034
[6] H. Kozono, Y. Maeda, and H. Naito: Global solutions for that Yang-Mills gradient flow on 4-manifolds. Nagoya Math. J., 139, 93-128 (1995). · Zbl 0849.58018
[7] M. Struwe : On the evolution of harmonic mappings of Riemann surfaces. Comm. Math. Helv., 4, 558-581 (1985). · Zbl 0595.58013 · doi:10.1007/BF02567432
[8] M. Struwe: The Yang-Mills flow in four dimensions. Calc. Var., 2, 123-150 (1994). · Zbl 0807.58010 · doi:10.1007/BF01191339
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.