The asymptotic behavior of Yang-Mills fields in the large. (English) Zbl 0767.53057

The paper is dealing with Yang-Mills equations \(F^{;\beta}_{\alpha\beta}=0\), \(^*F^{;\beta}_{\alpha\beta}=0\) in Minkowski space-time. Questions concerning global solutions in \(H^ s\) or global large solutions in the weighted Sobolev spaces \(H^{s,\delta}\) have already been known. Here, solutions corresponding to dipole-type Cauchy data are investigated. In particular, among other things, it is proved that all spherically symmetric solutions in the canonical gauge decay in time, if the initial data have finite conformal energy.


53Z05 Applications of differential geometry to physics
53C05 Connections (general theory)
81T13 Yang-Mills and other gauge theories in quantum field theory
Full Text: DOI


[1] Choquet-Bruhat, Y., Paneitz, S., Segal, I.: The Yang-Mills equations on the universal cosmos. J. Funct. Anal.53, 112 (1983) · Zbl 0535.58022
[2] Choquet-Bruhat, Y.: Lectures on global solutions of hyperbolic equations of gauge theories. Proceedings of Symposium at Simon Bolivar University, Caracas, Aragone, C. (ed.) · Zbl 0571.35087
[3] Christodoulou, D.: Solutions globales des equations de champs de Yang-Mills, C.R. Acad. Sci. Paris293, Ser. A, 39 (1981) · Zbl 0477.58038
[4] Eardley, D., Moncrief, V.: The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. Commun. Math. Phys.83, 171 (1982) · Zbl 0496.35061
[5] Georgiev, V.: Small-amplitude solutions of the Maxwell-Dirac equations. Indiana Univ. Math. J.40(3), 845 (1991) · Zbl 0754.35171
[6] Glassey, R.T., Strauss, W.A.: The Scattering of Yang-Mills fields. Commun. Math. Phys.89, 465 (1983) · Zbl 0527.35066
[7] Hawking, S., Ellis, G.: The large scale structure of space-time. Cambridge: Cambridge University Press 1978 · Zbl 0265.53054
[8] Jaffe, A., Taubes, C.: Vortices and monopoles. Birkhäuser Progress in Physics PPh2, New York, Basel: Birkhäuser 1980 · Zbl 0457.53034
[9] Klainerman, S.: The null condition and global existence to non-linear wave equations. Lectures in Applied Mathematics, Vol.23, Nicolaenko, B. (ed.), 1986 · Zbl 0599.35105
[10] Pecher, H.: Scattering for semilinear wave equations with small data in three space dimensions. Math. Zeit.198, 77 (1988) · Zbl 0627.35064
[11] Schirmer, P.P.: Global existence for spherically symmetric Yang-Mills fields on 3+1 spacetime dimensions. Doctoral dissertation, New York University, 1990
[12] Schirmer, P.P.: Decay estimates for spherically symmetric Yang-Mills fields in Minkowski space. Ann. Inst. Henri Poincaré, to appear
[13] Shu, W.T.: Commun. Math. Phys.140, 449–480 (1991) · Zbl 0735.53060
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.