Strichartz estimate and nonlinear Klein-Gordon on non-trapping scattering space

Abstract

We study the nonlinear Klein-Gordon equation on a product space $M=\mathbb{R}\times X$ with metric $\tilde{g}=d{t}^2-g$ where $g$ is the scattering metic on $X$. We establish the global-in-time Strichartz estimate for Klein-Gordon equation without loss of derivative by using the microlocalized spectral measure of Laplacian on scattering manifold showed in \cite{HZ} and a Littlewood-Paley squarefunction estimate proved in \cite{Zhang}. We prove the global existence and scattering for a family of nonlinear Klein-Gordon equations for small initial data with minimum regularity on this setting.

24 pages. arXiv admin note: text overlap with arXiv:1310.4564

References in corpus (1)

• Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces

Cited by in corpus (2)

• On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces
• Semiclassical limit of orthonormal Strichartz estimates on scattering manifolds