Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds

TL;DR

This paper establishes global Strichartz estimates for wave equations on nontrapping asymptotically conic manifolds, enabling proofs of global existence and scattering for certain nonlinear wave equations.

Contribution

It extends Strichartz estimates to a broad class of manifolds and includes endpoint cases, advancing understanding of wave behavior in geometric settings.

Findings

Proved global-in-time Strichartz estimates for wave equations.

Established global existence and scattering for nonlinear wave equations.

Utilized microlocal analysis and spectral measure properties.

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.