%0 Journal Article
%T The semilinear wave equation on asymptotically euclidean manifolds
%A Jean-Francois Bony
%A Dietrich Hafner
%J Mathematics
%D 2008
%I arXiv
%X We consider the quadratically semilinear wave equation on R^d, d>=3, equipped with a Riemannian metric. This metric is non-trapping and approaches the Euclidean metric polynomially at infinity. Using Mourre estimates and the Kato theory of smoothness, we obtain a Keel-Smith-Sogge type inequality for the linear equation. Thanks to this estimate, we prove long time existence (d=3) and global existence (d>3) for the nonlinear problem with small initial data.
%U http://arxiv.org/abs/0810.0464v1