Celebratio Mathematica — Choquet-Bruhat

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D. Bao, Y. Choquet-Bruhat, J. Isenberg, and P. B. Yasskin: “The well-posedness of (\( N=1 \)) classical supergravity,” J. Math. Phys. 26 : 2 (1985), pp. 329–333. MR 776502 Zbl 0563.53060 article

In this paper the authors investigate whether classical (\( N=1 \)) supergravity has a well-posed locally causal Cauchy problem. One defines well-posedness to mean that any choice of initial data (from an appropriate function space) which satisfies the supergravity constraint equations and a set of gauge conditions can be continuously developed into a space-time solution of the supergravity field equations around the initial surface. Local causally means that the domains of dependence of the evolution equations coincide with those determined by the light cones. They show that when the fields of classical supergravity are treated as formal objects, the field equations are (under certain gauge conditions) equivalent to a coupled system of quasilinear nondiagonal second-order partial differential equations which is formally nonstrictly hyperbolic (in the sense of Leray-Ohy). Hence, if the fields were numerical valued, there would be an applicable existence theorem leading to well-posedness.

James Allen Isenberg	Related
David Dai-Wai Bao	Related
Philip Barry Yasskin	Related