Polyhomogeneous solutions of nonlinear wave equations without corner conditions

Details Polyhomogeneous solutions of nonlinear wave equations without corner conditions Polyhomogeneous solutions of nonlinear wave equations without corner conditions

2005-06-21

arxiv.org/abs/math/0506423v2

Journal of Hyperbolic Differential Equations 3 (2006), 81-141

Mathematics

Analysis of PDEs

Minor corrections

Scientific paper

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

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