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

Access to Document

10.1007/s00526-019-1548-6

Cite this

@article{cb6457abdb204f03b6246c5727b077e7,

title = "Higher order Yang–Mills flow",

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 R{\aa}de (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.",

author = "Casey Kelleher",

note = "Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2019",

month = jun,

day = "1",

doi = "10.1007/s00526-019-1548-6",

language = "English (US)",

volume = "58",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Higher order Yang–Mills flow

AU - Kelleher, Casey

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85065902878

UR - https://www.scopus.com/inward/citedby.url?scp=85065902878&partnerID=8YFLogxK

U2 - 10.1007/s00526-019-1548-6

DO - 10.1007/s00526-019-1548-6

M3 - Article

AN - SCOPUS:85065902878

SN - 0944-2669

VL - 58

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 3

M1 - 100

ER -

Higher order Yang–Mills flow

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this