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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.

MSC:

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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