On blowup for Yang-Mills fields - INSPIRE

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On blowup for Yang-Mills fields

P. Bizon
(
- Potsdam, Max Planck Inst. and
- Jagiellonian U.
)
,
Z. Tabor
(
- Jagiellonian U.
)

May, 2001

4 pages

Published in:

Phys.Rev.D 64 (2001) 121701

e-Print:

math-ph/0105016 [math-ph]

DOI:

10.1103/PhysRevD.64.121701

Report number:

AEI-2001-50

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Abstract:

We study development of singularities for the spherically symmetric Yang-Mills equations in

d+1

dimensional Minkowski spacetime for

d=4

(the critical dimension) and

d=5

(the lowest supercritical dimension). Using combined numerical and analytical methods we show in both cases that generic solutions starting with sufficiently large initial data blow up in finite time. The mechanism of singularity formation depends on the dimension: in

d=5

the blowup is exactly self-similar while in

d=4

the blowup is only approximately self-similar and can be viewed as the adiabatic shrinking of the marginally stable static solution. The threshold for blowup and the connection with critical phenomena in the gravitational collapse (which motivated this research) are also briefly discussed.

Note:

4 pages, 3 figures, submitted to Physical Rview Letters Report-no: AEI-2001-50 Subj-class: Mathematical Physics; Analysis of PDEs MSC-class: 35Q99

gauge field theory: Yang-Mills
dimension: 5
dimension: 6
symmetry: rotation
field equations: solution
analytic properties
numerical calculations

References(12)

Figures(0)

THE GLOBAL EXISTENCE OF YANG-MILLS HIGGS FIELDS IN FOUR-DIMENSIONAL MINKOWSKI SPACE. 1. LOCAL EXISTENCE AND SMOOTHNESS PROPERTIES

D.M. Eardley
(
- Harvard U.
)
,
V. Moncrief
(
- Yale U.
)

- Commun.Math.Phys. 83 (1982) 171-191,
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•
DOI:
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- Annals Math. 142 39

Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields

T. Cazenave
(
- Paris U., VI-VII
)
,
J. Shatah
(
- New York U.
)
,
A.S. Tahvildar-Zadeh
(
- Princeton U., Plasma Physics Lab.
)

- Ann.Inst.H.Poincare Phys.Theor. 68 (1998) 315-349

Critical phenomena in gravitational collapse

Carsten Gundlach
(
- Potsdam, Max Planck Inst.
)

- Adv.Theor.Math.Phys. 2 (1998) 1-49
•
e-Print:
- gr-qc/9712084
•
DOI:
- 10.4310/ATMP.1998.v2.n1.a1

- Nonlinearity 14 1041

- Nonlinearity 13 1411

- Stud.Cerc.Mat. 34 329

Critical phenomena in nonlinear sigma models

- J.Math.Phys. 41 (2000) 5691-5700
•
e-Print:
- math-ph/9911020
•
DOI:
- 10.1063/1.533432

Fast blowup in the (4+1)-dimensional Yang-Mills model and the (2+1)-dimensional S**2 sigma model

Jean Marie Linhart

e-Print:
- math-ph/9909015

- Nonlinearity 12 1071

- SIAM J.Appl.Math. 60 183