Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds

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 [18] 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.