Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds
Analysis of PDEs
2014-12-02 v2
Abstract
We prove the global-in-time Strichartz estimates for wave equations on the nontrapping asymptotically conic manifolds. We obtain estimates for the full set of wave admissible indices, including the endpoint. The key points are the properties of the microlocalized spectral measure of Laplacian on this setting showed in Hassell-Zhang and a Littlewood-Paley squarefunction estimate. As applications, we prove the global existence and scattering for a family of nonlinear wave equations on this setting.
Keywords
Cite
@article{arxiv.1310.4564,
title = {Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds},
author = {Junyong Zhang},
journal= {arXiv preprint arXiv:1310.4564},
year = {2014}
}
Comments
To appear in Advances in Mathematics