  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.
