Vol. 9, No. 1, 2016

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Global-in-time Strichartz estimates on nontrapping, asymptotically conic manifolds

Andrew Hassell and Junyong Zhang

Vol. 9 (2016), No. 1, 151–192
DOI: 10.2140/apde.2016.9.151
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.

Keywords
Strichartz estimates, asymptotically conic manifolds, spectral measure, Schrödinger propagator
Mathematical Subject Classification 2010
Primary: 35Q41
Secondary: 58J40
Milestones
Received: 12 April 2015
Revised: 24 September 2015
Accepted: 28 October 2015
Published: 10 February 2016
Authors
Andrew Hassell
Department of Mathematics
Australian National University
Canberra ACT 2601
Australia
Junyong Zhang
Department of Mathematics
Beijing Institute of Technology
Beijing, 100081
China
Department of Mathematics
Australian National University
Canberra ACT 2601
Australia