The semilinear wave equation on asymptotically euclidean manifolds
Analysis of PDEs
2008-10-03 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.0810.0464,
title = {The semilinear wave equation on asymptotically euclidean manifolds},
author = {Jean-Francois Bony and Dietrich Hafner},
journal= {arXiv preprint arXiv:0810.0464},
year = {2008}
}
Comments
40 pages