Global-in-time Strichartz estimates on nontrapping, asymptotically conic manifolds

Abstract

We prove global-in-time Strichartz estimates without loss of derivatives for the solution of the Schrödinger equation on a class of nontrapping asymptotically conic manifolds. We obtain estimates for the full set of admissible indices, including the endpoint, in both the homogeneous and inhomogeneous cases. This result improves on the results by Tao, Wunsch and the first author and by Mizutani, which are local in time, as well as results of the second author, which are global in time but with a loss of angular derivatives. In addition, the endpoint inhomogeneous estimate is a strengthened version of the uniform Sobolev estimate recently proved by Guillarmou and the first author. The second author has proved similar results for the wave equation.