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2016 Global-in-time Strichartz estimates on nontrapping, asymptotically conic manifolds
Andrew Hassell, Junyong Zhang
Anal. PDE 9(1): 151-192 (2016). 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.

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Andrew Hassell. Junyong Zhang. "Global-in-time Strichartz estimates on nontrapping, asymptotically conic manifolds." Anal. PDE 9 (1) 151 - 192, 2016. https://doi.org/10.2140/apde.2016.9.151

Information

Received: 12 April 2015; Revised: 24 September 2015; Accepted: 28 October 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1333.35226
MathSciNet: MR3461304
Digital Object Identifier: 10.2140/apde.2016.9.151

Subjects:
Primary: 35Q41
Secondary: 58J40

Keywords: asymptotically conic manifolds , Schrödinger propagator , spectral measure , Strichartz estimates

Rights: Copyright © 2016 Mathematical Sciences Publishers

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