Linear and nonlinear field equations. (English) Zbl 0653.35079

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 14, 8 p. (1987).
The aim of this lecture is to illustrate how some recent geometric techniques which were usual to derive global existence and long time existence results for nonlinear wave equations [see the author, Commun. Pure Appl. Math. 38, 321-332 (1985; Zbl 0635.35059) and Lect. Appl. Math. 23, Pt. 1, 293-326 (1986; Zbl 0599.35105); and D. Christodoulou, Commun. Pure Appl. Math. 39, 267-282 (1986; Zbl 0612.35090)] can be applied to tensorial field equations. We limitate ourselves here in describing the results which we have obtained in colloboration with D. Christodoulou, to the linear Maxwell and Spin-2 equations in Minkowski space [see D. Christodoulou and the author, Uniform decay estimates for linear field equations in Minkowski space (preprint)]. The latter are a linearised version of the Einstein equations in vacuum and their study important in our attempt to prove the global nonlinear stability of the Minkowski metric.


35Q99 Partial differential equations of mathematical physics and other areas of application
81T08 Constructive quantum field theory
35A30 Geometric theory, characteristics, transformations in context of PDEs
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