Higher order Yang–Mills flow

Casey Kelleher

doi:10.1007/s00526-019-1548-6

Higher order Yang–Mills flow

Casey Kelleher

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We define a family of functionals generalizing the Yang–Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for critical dimensions. Consequently, we generalize the results of the convergence of Yang–Mills flow in dimensions 2 and 3 given by Råde (J Reine Angew Math 431:123–163, 1992) and the bubbling criterion in dimension 4 of Struwe (Calc Var 2:123–150, 1994) in the case where the initial flow data is smooth.

Original language	English (US)
Article number	100
Journal	Calculus of Variations and Partial Differential Equations
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s00526-019-1548-6
State	Published - Jun 1 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00526-019-1548-6

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AB - We define a family of functionals generalizing the Yang–Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for critical dimensions. Consequently, we generalize the results of the convergence of Yang–Mills flow in dimensions 2 and 3 given by Råde (J Reine Angew Math 431:123–163, 1992) and the bubbling criterion in dimension 4 of Struwe (Calc Var 2:123–150, 1994) in the case where the initial flow data is smooth.

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ER -

Higher order Yang–Mills flow

Abstract

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